Lanczos-Boosted Numerical Linked-Cluster Expansion For Quantum Lattice Models, Krishnakumar Bhattaram, Ehsan Khatami
Jul 2019
Lanczos-Boosted Numerical Linked-Cluster Expansion For Quantum Lattice Models, Krishnakumar Bhattaram, Ehsan Khatami
Ehsan Khatami
Numerical linked-cluster expansions allow one to calculate finite-temperature properties of quantum lattice models directly in the thermodynamic limit through exact solutions of small clusters. However, full diagonalization is often the limiting factor for these calculations. Here we show that a partial diagonalization of the largest clusters in the expansion using the Lanczos algorithm can be as useful as full diagonalization for the method while mitigating some of the time and memory issues. As test cases, we consider the frustrated Heisenberg model on the checkerboard lattice and the Fermi-Hubbard model on the square lattice. We find that our approach can surpass ...
Unconventional Pairing Symmetry Of Interacting Dirac Fermions On A Π -Flux Lattice, Huaiming Guo, Ehsan Khatami, Yao Wang, Thomas P. Devereaux, Rajiv R.P. Singh, Richard T. Scalettar
Apr 2018
Unconventional Pairing Symmetry Of Interacting Dirac Fermions On A Π -Flux Lattice, Huaiming Guo, Ehsan Khatami, Yao Wang, Thomas P. Devereaux, Rajiv R.P. Singh, Richard T. Scalettar
Ehsan Khatami
The pairing symmetry of interacting Dirac fermions on the π-flux lattice is studied with the determinant quantum Monte Carlo and numerical linked-cluster expansion methods. The s∗- (i.e., extended s-) and d-wave pairing symmetries, which are distinct in the conventional square lattice, are degenerate under the Landau gauge. We demonstrate that the dominant pairing channel at strong interactions is an unconventional ds∗-wave phase consisting of alternating stripes of s∗- and d-wave phases. A complementary mean-field analysis shows that while the s∗- and d-wave symmetries individually have nodes in the energy spectrum, the ds∗ channel is ...
Unsupervised Machine Learning Account Of Magnetic Transitions In The Hubbard Model, Kelvin Ch'ng, Nick Vazquez, Ehsan Khatami
Dec 2017
Unsupervised Machine Learning Account Of Magnetic Transitions In The Hubbard Model, Kelvin Ch'ng, Nick Vazquez, Ehsan Khatami
Ehsan Khatami
We employ several unsupervised machine learning techniques, including autoencoders, random trees embedding, and t-distributed stochastic neighboring ensemble (t-SNE), to reduce the dimensionality of, and therefore classify, raw (auxiliary) spin configurations generated, through Monte Carlo simulations of small clusters, for the Ising and Fermi-Hubbard models at finite temperatures. Results from a convolutional autoencoder for the three-dimensional Ising model can be shown to produce the magnetization and the susceptibility as a function of temperature with a high degree of accuracy. Quantum fluctuations distort this picture and prevent us from making such connections between the output of the autoencoder and physical ...
Spin-Imbalance In A 2d Fermi-Hubbard System, Peter T. Brown, Debayan Mitra, Elmer Guardado-Sanchez, Peter Schauß, Stanimir S. Kondov, Ehsan Khatami, Thereza Paiva, Nandini Trivedi, David A. Huse, Waseem S. Bakr
Sep 2017
Spin-Imbalance In A 2d Fermi-Hubbard System, Peter T. Brown, Debayan Mitra, Elmer Guardado-Sanchez, Peter Schauß, Stanimir S. Kondov, Ehsan Khatami, Thereza Paiva, Nandini Trivedi, David A. Huse, Waseem S. Bakr
Ehsan Khatami
The interplay of strong interactions and magnetic fields gives rise to unusual forms of superconductivity and magnetism in quantum many-body systems. Here, we present an experimental study of the two-dimensional Fermi-Hubbard model—a paradigm for strongly correlated fermions on a lattice—in the presence of a Zeeman field and varying doping. Using site-resolved measurements, we revealed anisotropic antiferromagnetic correlations, a precursor to long-range canted order. We observed nonmonotonic behavior of the local polarization with doping for strong interactions, which we attribute to the evolution from an antiferromagnetic insulator to a metallic phase. Our results pave the way to experimentally mapping ...
Machine Learning Phases Of Strongly Correlated Fermions, Kelvin Ch'ng, Juan Carrasquilla, Roger G. Melko, Ehsan Khatami
Aug 2017
Machine Learning Phases Of Strongly Correlated Fermions, Kelvin Ch'ng, Juan Carrasquilla, Roger G. Melko, Ehsan Khatami
Ehsan Khatami
Machine learning offers an unprecedented perspective for the problem of classifying phases in condensed matter physics. We employ neural network machine learning techniques to distinguish finite-temperature phases of the strongly-correlated fermions on cubic lattices. We show that a three-dimensional convolutional network trained on auxiliary field configurations produced by quantum Monte Carlo simulations of the Hubbard model can correctly predict the magnetic phase diagram of the model at the average density of one (half filling). We then use the network, trained at half filling, to explore the trend in the transition temperature as the system is doped away from half filling ...
Competing Phases And Orbital-Selective Behaviors In The Two-Orbital Hubbard-Holstein Model, Shaozhi Li, Ehsan Khatami, Steven Johnston
Mar 2017
Competing Phases And Orbital-Selective Behaviors In The Two-Orbital Hubbard-Holstein Model, Shaozhi Li, Ehsan Khatami, Steven Johnston
Ehsan Khatami
We study the interplay between the electron-electron (e-e) and the electron-phonon (e-ph) interactions in the two-orbital Hubbard-Holstein model at half-filling using the dynamical mean-field theory. We find that the e-ph interaction, even at weak couplings, strongly modifies the phase diagram of this model and introduces an orbital-selective Peierls insulating phase (OSPI) that is analogous to the widely studied orbital-selective Mott phase (OSMP). At small e-e and e-ph couplings, we find a competition between the OSMP and the OSPI, while at large couplings, a competition occurs between Mott and charge-density-wave (CDW) insulating phases. We further demonstrate that the Hund's coupling ...
Competing Phases And Orbital-Selective Behaviors In The Two-Orbital Hubbard-Holstein Model, Shaozhi Li, Ehsan Khatami, Steven Johnston
Dec 2016
Competing Phases And Orbital-Selective Behaviors In The Two-Orbital Hubbard-Holstein Model, Shaozhi Li, Ehsan Khatami, Steven Johnston
Ehsan Khatami
We study the interplay between the electron-electron (e-e) and the electron-phonon (e-ph) interactions in the two-orbital Hubbard-Holstein model at half filling using the dynamical mean field theory. We find that the e-ph interaction, even at weak couplings, strongly modifies the phase diagram of this model and introduces an orbital-selective Peierls insulating phase (OSPI) that is analogous to the widely studied orbital-selective Mott phase (OSMP). At small e-e and e-ph coupling, we find a competition between the OSMP and the OSPI, while at large couplings, a competition occurs between Mott and charge-density-wave (CDW) insulating phases. We further demonstrate that the Hund ...
Transport And Optical Conductivity In The Hubbard Model: A High-Temperature Expansion Perspective, Edward Perepelitsky, Andrew Galatas, Jernej Mravlje, Rok Žitko, Ehsan Khatami, B. Sriram Shastry, Antoine Georges
Nov 2016
Transport And Optical Conductivity In The Hubbard Model: A High-Temperature Expansion Perspective, Edward Perepelitsky, Andrew Galatas, Jernej Mravlje, Rok Žitko, Ehsan Khatami, B. Sriram Shastry, Antoine Georges
Ehsan Khatami
We derive analytical expressions for the spectral moments of the dynamical response functions of the Hubbard model using the high-temperature series expansion. We consider generic dimension d as well as the infinite-d limit, arbitrary electron density n, and both finite and infinite repulsion U. We use moment-reconstruction methods to obtain the one-electron spectral function, the self-energy, and the optical conductivity. They are all smooth functions at high temperature and, at large U, they are featureless with characteristic widths of the order of the lattice hopping parameter t. In the infinite-d limit, we compare the series expansion results with ...
Observation Of Spatial Charge And Spin Correlations In The 2d Fermi-Hubbard Model, Lawrence W. Cheuk, Matthew A. Nichols, Katherine R. Lawrence, Melih Okan, Hao Zhang, Ehsan Khatami, Nandini Trivedi, Thereza Paiva, Marcos Rigol, Martin W. Zwierlein
Sep 2016
Observation Of Spatial Charge And Spin Correlations In The 2d Fermi-Hubbard Model, Lawrence W. Cheuk, Matthew A. Nichols, Katherine R. Lawrence, Melih Okan, Hao Zhang, Ehsan Khatami, Nandini Trivedi, Thereza Paiva, Marcos Rigol, Martin W. Zwierlein
Ehsan Khatami
Strong electron correlations lie at the origin of high-temperature superconductivity. Its essence is believed to be captured by the Fermi-Hubbard model of repulsively interacting fermions on a lattice. Here we report on the site-resolved observation of charge and spin correlations in the two-dimensional (2D) Fermi-Hubbard model realized with ultracold atoms. Antiferromagnetic spin correlations are maximal at half-filling and weaken monotonically upon doping. At large doping, nearest-neighbor correlations between singly charged sites are negative, revealing the formation of a correlation hole, the suppressed probability of finding two fermions near each other. As the doping is reduced, the correlations become positive, signaling ...
Three-Dimensional Hubbard Model In The Thermodynamic Limit, Ehsan Khatami
Aug 2016
Three-Dimensional Hubbard Model In The Thermodynamic Limit, Ehsan Khatami
Ehsan Khatami
We employ the numerical linked-cluster expansion to study finite-temperature properties of the uniform cubic lattice Hubbard model in the thermodynamic limit for a wide range of interaction strengths and densities. We carry out the expansion to the 9th order and find that the convergence of the series extends to lower temperatures as the strength of the interaction increases, giving us access to regions of the parameter space that are difficult to reach by most other numerical methods. We study the precise trends in the specific heat, the double occupancy, and magnetic correlations at temperatures as low as 0.2 of ...
Observation Of Canted Antiferromagnetism With Ultracold Fermions In An Optical Lattice, Peter T. Brown, Debayan Mitra, Elmer Guardado-Sanchez, Peter Schauß, Stanimir S. Kondov, Ehsan Khatami, Thereza Paiva, Nandini Trivedi, David A. Huse, Waseem S. Bakr
Dec 2015
Observation Of Canted Antiferromagnetism With Ultracold Fermions In An Optical Lattice, Peter T. Brown, Debayan Mitra, Elmer Guardado-Sanchez, Peter Schauß, Stanimir S. Kondov, Ehsan Khatami, Thereza Paiva, Nandini Trivedi, David A. Huse, Waseem S. Bakr
Ehsan Khatami
Understanding the magnetic response of the normal state of the cuprates is considered a key piece in solving the puzzle of their high-temperature superconductivity. The essential physics of these materials is believed to be captured by the Fermi-Hubbard model, a minimal model that has been realized with cold atoms in optical lattices. Here we report on site-resolved measurements of the Fermi-Hubbard model in a spin-imbalanced atomic gas, allowing us to explore the response of the system to large effective magnetic fields. We observe short-range canted antiferromagnetism at half-filling with stronger spin correlations in the direction orthogonal to the magnetization, in ...
Observation Of Antiferromagnetic Correlations In The Hubbard Model With Ultracold Atoms, Russell A. Hart, Pedro M. Duarte, Tsung-Lin Yang, Xinxing Liu, Thereza Paiva, Ehsan Khatami, Richard T. Scalettar, Nandini Trivedi, David A. Huse, Randall G. Hulet
Mar 2015
Observation Of Antiferromagnetic Correlations In The Hubbard Model With Ultracold Atoms, Russell A. Hart, Pedro M. Duarte, Tsung-Lin Yang, Xinxing Liu, Thereza Paiva, Ehsan Khatami, Richard T. Scalettar, Nandini Trivedi, David A. Huse, Randall G. Hulet
Ehsan Khatami
Ultracold atoms in optical lattices have great potential to contribute to a better understanding of some of the most important issues in many-body physics, such as high-temperature superconductivity. The Hubbard model—a simplified representation of fermions moving on a periodic lattice—is thought to describe the essential details of copper oxide superconductivity. This model describes many of the features shared by the copper oxides, including an interaction-driven Mott insulating state and an antiferromagnetic (AFM) state. Optical lattices filled with a two-spin-component Fermi gas of ultracold atoms can faithfully realize the Hubbard model with readily tunable parameters, and thus provide a ...
Compressibility Of A Fermionic Mott Insulator Of Ultracold Atoms, Pedro M. Duarte, Russell A. Hart, Tsung-Lin Yang, Xinxing Liu, Thereza Paiva, Ehsan Khatami, Richard T. Scalettar, Nandini Trivedi, Randall G. Hulet
Jan 2015
Compressibility Of A Fermionic Mott Insulator Of Ultracold Atoms, Pedro M. Duarte, Russell A. Hart, Tsung-Lin Yang, Xinxing Liu, Thereza Paiva, Ehsan Khatami, Richard T. Scalettar, Nandini Trivedi, Randall G. Hulet
Ehsan Khatami
We characterize the Mott insulating regime of a repulsively interacting Fermi gas of ultracold atoms in a three-dimensional optical lattice. We use in situ imaging to extract the central density of the gas and to determine its local compressibility. For intermediate to strong interactions, we observe the emergence of a plateau in the density as a function of atom number, and a reduction of the compressibility at a density of one atom per site, indicating the formation of a Mott insulator. Comparisons to state-of-the-art numerical simulations of the Hubbard model over a wide range of interactions reveal that the temperature ...
Finite-Temperature Superconducting Correlations Of The Hubbard Model, Ehsan Khatami, Richard T. Scalettar, Rajiv R.P. Singh
Dec 2014
Finite-Temperature Superconducting Correlations Of The Hubbard Model, Ehsan Khatami, Richard T. Scalettar, Rajiv R.P. Singh
Ehsan Khatami
We utilize numerical linked-cluster expansions (NLCEs) and the determinantal quantum Monte Carlo algorithm to study pairing correlations in the square-lattice Hubbard model. To benchmark the NLCE, we first locate the finite-temperature phase transition of the attractive model to a superconducting state away from half filling. We then explore the superconducting properties of the repulsive model for the d-wave and extended s-wave pairing symmetries. The pairing structure factor shows a strong tendency to d-wave pairing and peaks at an interaction strength comparable to the bandwidth. The extended s-wave structure factor and correlation length are larger at higher temperatures but clearly saturate ...
Geometry Dependence Of The Sign Problem In Quantum Monte Carlo Simulations, V. I. Iglovikov, Ehsan Khatami, R. T. Scalettar
Dec 2014
Geometry Dependence Of The Sign Problem In Quantum Monte Carlo Simulations, V. I. Iglovikov, Ehsan Khatami, R. T. Scalettar
Ehsan Khatami
The sign problem is the fundamental limitation to quantum Monte Carlo simulations of the statistical mechanics of interacting fermions. Determinant quantum Monte Carlo (DQMC) is one of the leading methods to study lattice fermions, such as the Hubbard Hamiltonian, which describe strongly correlated phenomena including magnetism, metal-insulator transitions, and possibly exotic superconductivity. Here, we provide a comprehensive dataset on the geometry dependence of the DQMC sign problem for different densities, interaction strengths, temperatures, and spatial lattice sizes. We supplement these data with several observations concerning general trends in the data, including the dependence on spatial volume and how this can ...
Magnetic Correlations And Pairing In The 1/5-Depleted Square Lattice Hubbard Model, Ehsan Khatami, Rajiv R.P. Singh, Warren E. Pickett, Richard T. Scalettar
Dec 2013
Magnetic Correlations And Pairing In The 1/5-Depleted Square Lattice Hubbard Model, Ehsan Khatami, Rajiv R.P. Singh, Warren E. Pickett, Richard T. Scalettar
Ehsan Khatami
We study the single-orbital Hubbard model on the 1/5-depleted square-lattice geometry, which arises in such diverse systems as the spin-gap magnetic insulator CaV4O9 and ordered-vacancy iron selenides, presenting new issues regarding the origin of both magnetic ordering and superconductivity in these materials. We find a rich phase diagram that includes a plaquette singlet phase, a dimer singlet phase, a Néel and a block-spin antiferromagnetic phase, and stripe phases. Quantum Monte Carlo simulations show that the dominant pairing correlations at half filling change character from d wave in the plaquette phase to extended s wave upon transition to the Néel ...
Linked-Cluster Expansion For The Green's Function Of The Infinite-U Hubbard Model, Ehsan Khatami, Edward Perepelitsky, Marcos Rigol, Sriram B. Shastry
Dec 2013
Linked-Cluster Expansion For The Green's Function Of The Infinite-U Hubbard Model, Ehsan Khatami, Edward Perepelitsky, Marcos Rigol, Sriram B. Shastry
Ehsan Khatami
We implement a highly efficient strong-coupling expansion for the Green's function of the Hubbard model. In the limit of extreme correlations, where the onsite interaction is infinite, the evaluation of diagrams simplifies dramatically enabling us to carry out the expansion to the eighth order in powers of the hopping amplitude. We compute the finite-temperature Green's function analytically in the momentum and Matsubara frequency space as a function of the electron density. Employing Padé approximations, we study the equation of state, Kelvin thermopower, momentum distribution function, quasiparticle fraction, and quasiparticle lifetime of the system at temperatures lower than, or ...
Fluctuation-Dissipation Theorem In Isolated Quantum Systems Out Of Equilibrium, Ehsan Khatami, Guido Pupillo, Mark Srednicki, Marcos Rigol
Dec 2013
Fluctuation-Dissipation Theorem In Isolated Quantum Systems Out Of Equilibrium, Ehsan Khatami, Guido Pupillo, Mark Srednicki, Marcos Rigol
Ehsan Khatami
We study the validity of the fluctuation-dissipation theorem for an isolated quantum system of harmonically trapped dipolar molecules taken out of equilibrium by means of a quench, a sudden change in the Hamiltonian parameters. We find that the integrability of the system plays a crucial role in the validity of the fluctuation-dissipation theorem. Namely, the system thermalizes according to the eigenstate thermalization hypothesis and the theorem holds if the system is nonintegrable after the quench. However, it fails if the system is integrable, unless the initial state is an eigenstate of a nonintegrable Hamiltonian, in which case the system still ...
Finite-Temperature Properties Of Strongly Correlated Fermions In The Honeycomb Lattice, Baoming Tang, Thereza Paiva, Ehsan Khatami, Marchos Rigol
Sep 2013
Finite-Temperature Properties Of Strongly Correlated Fermions In The Honeycomb Lattice, Baoming Tang, Thereza Paiva, Ehsan Khatami, Marchos Rigol
Ehsan Khatami
We study finite-temperature properties of strongly interacting fermions in the honeycomb lattice using numerical linked-cluster expansions and determinantal quantum Monte Carlo simulations. We analyze a number of thermodynamic quantities, including the entropy, the specific heat, uniform and staggered spin susceptibilities, short-range spin correlations, and the double occupancy at and away from half filling. We examine the viability of adiabatic cooling by increasing the interaction strength for homogeneous as well as for trapped systems. For the homogeneous case, this process is found to be more efficient at finite doping than at half filling. That, in turn, leads to an efficient adiabatic ...
Electronic Spectral Properties Of The Two-Dimensional Infinite-U Hubbard Model, Ehsan Khatami, Daniel Hansen, Edward Perepelitsky, Marcos Rigol, Sriram B. Shastry
Mar 2013
Electronic Spectral Properties Of The Two-Dimensional Infinite-U Hubbard Model, Ehsan Khatami, Daniel Hansen, Edward Perepelitsky, Marcos Rigol, Sriram B. Shastry
Ehsan Khatami
A strong-coupling series expansion for the Green's function and the extremely correlated Fermi liquid (ECFL) theory are used to calculate the moments of the electronic spectral functions of the infinite-U Hubbard model. Results from these two complementary methods agree very well at both low densities, where the ECFL solution is the most accurate, and at high to intermediate temperatures, where the series converge. We find that a modified first moment, which underestimates the contributions from the occupied states and is accessible in the series through the time-dependent Green's function, best describes the peak location of the spectral function ...
A Short Introduction To Numerical Linked-Cluster Expansions, Baoming Tang, Ehsan Khatami, Marcos Rigol
Feb 2013
A Short Introduction To Numerical Linked-Cluster Expansions, Baoming Tang, Ehsan Khatami, Marcos Rigol
Ehsan Khatami
We provide a pedagogical introduction to numerical linked-cluster expansions (NLCEs). We sketch the algorithm for generic Hamiltonians that only connect nearest-neighbor sites in a finite cluster with open boundary conditions. We then compare results for a specific model, the Heisenberg model, in each order of the NLCE with the ones for the finite cluster calculated directly by means of full exact diagonalization. We discuss how to reduce the computational cost of the NLCE calculations by taking into account symmetries and topologies of the linked clusters. Finally, we generalize the algorithm to the thermodynamic limit, and discuss several numerical resummation techniques ...
Fluctuation-Dissipation Theorem In An Isolated System Of Quantum Dipolar Bosons After A Quench, Ehsan Khatami, Guido Pupillo, Mark Srednicki, Marcos Rigol
Dec 2012
Fluctuation-Dissipation Theorem In An Isolated System Of Quantum Dipolar Bosons After A Quench, Ehsan Khatami, Guido Pupillo, Mark Srednicki, Marcos Rigol
Ehsan Khatami
We examine the validity of fluctuation-dissipation relations in isolated quantum systems taken out of equilibrium by a sudden quench. We focus on the dynamics of trapped hard-core bosons in one-dimensional lattices with dipolar interactions whose strength is changed during the quench. We find indications that fluctuation-dissipation relations hold if the system is nonintegrable after the quench, as well as if it is integrable after the quench if the initial state is an equilibrium state of a nonintegrable Hamiltonian. On the other hand, we find indications that they fail if the system is integrable both before and after quenching.
Effect Of Particle Statistics In Strongly Correlated Two-Dimensional Hubbard Models, Ehsan Khatami, Marcos Rigol
Jul 2012
Effect Of Particle Statistics In Strongly Correlated Two-Dimensional Hubbard Models, Ehsan Khatami, Marcos Rigol
Ehsan Khatami
We study the onset of particle statistics effects as the temperature is lowered in strongly correlated two-dimensional Hubbard models. We utilize numerical linked-cluster expansions and focus on the properties of interacting lattice fermions and two-component hard-core bosons. In the weak-coupling regime, where the ground state of the bosonic system is a superfluid, the thermodynamic properties of the two systems at half filling exhibit very large differences even at high temperatures. In the strong-coupling regime, where the low-temperature behavior is governed by a Mott insulator for either particle statistics, the agreement between the thermodynamic properties of both systems extends to regions ...
Quantum Quenches In Disordered Systems: Approach To Thermal Equilibrium Without A Typical Relaxation Time, Ehsan Khatami, Marcos Rigol, Armando Relaño, Antonio M. García-García
Apr 2012
Quantum Quenches In Disordered Systems: Approach To Thermal Equilibrium Without A Typical Relaxation Time, Ehsan Khatami, Marcos Rigol, Armando Relaño, Antonio M. García-García
Ehsan Khatami
We study spectral properties and the dynamics after a quench of one-dimensional spinless fermions with short-range interactions and long-range random hopping. We show that a sufficiently fast decay of the hopping term promotes localization effects at finite temperature, which prevents thermalization even if the classical motion is chaotic. For slower decays, we find that thermalization does occur. However, within this model, the latter regime falls in an unexpected universality class, namely, observables exhibit a power-law (as opposed to an exponential) approach to their thermal expectation values.
Numerical Study Of The Thermodynamics Of Clinoatacamite, Ehsan Khatami, Joel S. Helton, Marcos Rigol
Jan 2012
Numerical Study Of The Thermodynamics Of Clinoatacamite, Ehsan Khatami, Joel S. Helton, Marcos Rigol
Ehsan Khatami
We study the thermodynamic properties of the clinoatacamite compound, Cu2(OH)3Cl, by considering several approximate models. They include the Heisenberg model on (i) the uniform pyrochlore lattice, (ii) a very anisotropic pyrochlore lattice, and (iii) a kagome lattice weakly coupled to spins that sit on a triangular lattice. We utilize the exact diagonalization of small clusters with periodic boundary conditions and implement a numerical linked-cluster expansion approach for quantum lattice models with reduced symmetries, which allows us to solve model (iii) in the thermodynamic limit. We find a very good agreement between the experimental uniform susceptibility and the numerical ...
Numerical Linked-Cluster Expansion For The Distorted Kagome Lattice Heisenberg Model, Ehsan Khatami, Marcos Rigol
Dec 2011
Numerical Linked-Cluster Expansion For The Distorted Kagome Lattice Heisenberg Model, Ehsan Khatami, Marcos Rigol
Ehsan Khatami
Motivated by experimental results for the thermodynamic properties of the Rb2Cu3SnF12 material and the discovery of its valence-bond solid ground state, we utilize the numerical linked-cluster expansions (NLCEs) and devise an expansion tailored to solve the Heisenberg model on a pinwheel-distorted kagome lattice. Using the exchange interactions that are relevant to Rb2Cu3SnF12, we calculate its uniform spin susceptibility and find a very good agreement with experiment. Next, we focus on the ground state of a simplified model of the distorted kagome lattice and take advantage of a zero-temperature Lanczos-based NLCE to study the approach to the ground state of the ...
Short-Range Correlations And Cooling Of Ultracold Fermions In The Honeycomb Lattice, Baoming Tang, Thereza Paiva, Ehsan Khatami, Marcos Rigol
Dec 2011
Short-Range Correlations And Cooling Of Ultracold Fermions In The Honeycomb Lattice, Baoming Tang, Thereza Paiva, Ehsan Khatami, Marcos Rigol
Ehsan Khatami
We use determinantal quantum Monte Carlo simulations and numerical linked-cluster expansions to study thermodynamic properties and short-range spin correlations of fermions in the honeycomb lattice. We find that, at half filling and finite temperatures, nearest-neighbor spin correlations can be stronger in this lattice than in the square lattice, even in regimes where the ground state in the former is a semimetal or a spin liquid. The honeycomb lattice also exhibits a more pronounced anomalous region in the double occupancy that leads to stronger adiabatic cooling than in the square lattice. We discuss the implications of these findings for optical lattice ...
Thermodynamics And Phase Transitions For The Heisenberg Model On The Pinwheel Distorted Kagome Lattice, Ehsan Khatami, Rajiv R.P. Singh, Marcos Rigol
Nov 2011
Thermodynamics And Phase Transitions For The Heisenberg Model On The Pinwheel Distorted Kagome Lattice, Ehsan Khatami, Rajiv R.P. Singh, Marcos Rigol
Ehsan Khatami
We study the Heisenberg model on the pinwheel distorted kagome lattice as observed in the material Rb2Cu3SnF12. Experimentally relevant thermodynamic properties at finite temperatures are computed utilizing numerical linked-cluster expansions. We also develop a Lanczos-based, zero-temperature, numerical linked-cluster expansion to study the approach of the pinwheel distorted lattice to the uniform kagome-lattice Heisenberg model. We find strong evidence for a phase transition before the uniform limit is reached, implying that the ground state of the kagome-lattice Heisenberg model is likely not pinwheel dimerized and is stable to finite pinwheel-dimerizing perturbations.
Thermodynamics Of Strongly Interacting Fermions In Two-Dimensional Optical Lattices, Ehsan Khatami, Marcos Rigol
Oct 2011
Thermodynamics Of Strongly Interacting Fermions In Two-Dimensional Optical Lattices, Ehsan Khatami, Marcos Rigol
Ehsan Khatami
We study finite-temperature properties of strongly correlated fermions in two-dimensional optical lattices by means of numerical linked cluster expansions, a computational technique that allows one to obtain exact results in the thermodynamic limit. We focus our analysis on the strongly interacting regime, where the on-site repulsion is of the order of or greater than the band width. We compute the equation of state, double occupancy, entropy, uniform susceptibility, and spin correlations for temperatures that are similar to or below the ones achieved in current optical lattice experiments. We provide a quantitative analysis of adiabatic cooling of trapped fermions in two ...
Thermodynamics Of The Antiferromagnetic Heisenberg Model On The Checkerboard Lattice, Ehsan Khatami, Maros Rigol
Mar 2011
Thermodynamics Of The Antiferromagnetic Heisenberg Model On The Checkerboard Lattice, Ehsan Khatami, Maros Rigol
Ehsan Khatami
Employing numerical linked-cluster expansions (NLCEs) along with exact diagonalizations of finite clusters with periodic boundary condition, we study the energy, specific heat, entropy, and various susceptibilities of the antiferromagnetic Heisenberg model on the checkerboard lattice. NLCEs, combined with extrapolation techniques, allow us to access temperatures much lower than those accessible to exact diagonalization and other series expansions. We show that the high-temperature peak in specific heat decreases as the frustration increases, consistent with the large amount of unquenched entropy in the region around maximum classical frustration, where the nearest-neighbor and next-nearest-neighbor exchange interactions (J and J′, respectively) have the same ...