Nonanalytic Magnetization Dependence Of The Magnon Effective Mass In Itinerant Quantum Ferromagnets, 2018 Missouri University of Science and Technology

#### Nonanalytic Magnetization Dependence Of The Magnon Effective Mass In Itinerant Quantum Ferromagnets, Dietrich Belitz, Theodore R. Kirkpatrick, Andrew J. Millis, Thomas Vojta

*Thomas Vojta*

The spin-wave dispersion relation in both clean and disordered itinerant quantum ferromagnets is calculated. It is found that effects akin to weak-localization physics cause the frequency of the spin waves to be a *nonanalytic* function of the magnetization *m*. For low frequencies Ω, small wave vectors k, and m→0, the dispersion relation is found to be of the form Ω=const x m^{1-α}k^{2}, with α = (4-d)/2 (2 < d < 4) for disordered systems, and α = (3-d) (1 < d < 3) for clean ones. In d = 4 (disordered) and d = 3 (clean), Ωα*m *ln (1/*m*) k^{2}. Experiments to test these predictions are proposed.

Nonanalytic Behavior Of The Spin Susceptibility In Clean Fermi Systems, 2018 Missouri University of Science and Technology

#### Nonanalytic Behavior Of The Spin Susceptibility In Clean Fermi Systems, Dietrich Belitz, Theodore R. Kirkpatrick, Thomas Vojta

*Thomas Vojta*

The wave vector and temperature-dependent static spin susceptibility, Xs(Q, T), of clean interacting Fermi systems is considered in dimensions 1 ≤ d ≤ 3. We show that at zero temperature Xs is a nonanalytic function of |Q|, with the leading nonanalyticity being |Q|d-1 for 1 < d < 3, and Q2ln|Q| for d = 3. For the homogeneous spin susceptibility we find a nonanalytic temperature dependence Td-1 for 1 < d < 3. We give qualitative mode-mode coupling arguments to that effect, and corroborate these arguments by a perturbative calculation to second order in the electron-electron interaction amplitude. The implications of this, in particular ...

Monte Carlo Simulations Of The Clean And Disordered Contact Process In Three Dimensions, 2018 Missouri University of Science and Technology

#### Monte Carlo Simulations Of The Clean And Disordered Contact Process In Three Dimensions, Thomas Vojta

*Thomas Vojta*

The absorbing-state transition in the three-dimensional contact process with and without quenched randomness is investigated by means of Monte Carlo simulations. In the clean case, a reweighting technique is combined with a careful extrapolation of the data to infinite time to determine with high accuracy the critical behavior in the three-dimensional directed percolation universality class. In the presence of quenched spatial disorder, our data demonstrate that the absorbing-state transition is governed by an unconventional infinite-randomness critical point featuring activated dynamical scaling. The critical behavior of this transition does not depend on the disorder strength, i.e., it is universal. Close ...

Monte Carlo Simulations Of The Disordered Three-Color Quantum Ashkin-Teller Chain, 2018 Missouri University of Science and Technology

#### Monte Carlo Simulations Of The Disordered Three-Color Quantum Ashkin-Teller Chain, Ahmed K. Ibrahim, Thomas Vojta

*Thomas Vojta*

We investigate the zero-temperature quantum phase transitions of the disordered three-color quantum Ashkin-Teller spin chain by means of large-scale Monte Carlo simulations. We find that the first-order phase transitions of the clean system are rounded by the quenched disorder. For weak intercolor coupling, the resulting emergent quantum critical point between the paramagnetic phase and the magnetically ordered Baxter phase is of infinite-randomness type and belongs to the universality class of the random transverse-field Ising model, as predicted by recent strong-disorder renormalization group calculations. We also find evidence for unconventional critical behavior in the case of strong intercolor coupling, even though ...

Percolation Transition In Quantum Ising And Rotor Models With Sub-Ohmic Dissipation, 2018 Missouri University of Science and Technology

#### Percolation Transition In Quantum Ising And Rotor Models With Sub-Ohmic Dissipation, Manal Al-Ali, Jose Abel Hoyos, Thomas Vojta

*Thomas Vojta*

We investigate the influence of sub-Ohmic dissipation on randomly diluted quantum Ising and rotor models. The dissipation causes the quantum dynamics of sufficiently large percolation clusters to freeze completely. As a result, the zero-temperature quantum phase transition across the lattice percolation threshold separates an unusual super-paramagnetic cluster phase from an inhomogeneous ferromagnetic phase. We determine the low-temperature thermodynamic behavior in both phases, which is dominated by large frozen and slowly fluctuating percolation clusters. We relate our results to the smeared transition scenario for disordered quantum phase transitions, and we compare the cases of sub-Ohmic, Ohmic, and super-Ohmic dissipation.

Magnetic Excitations In The Spinel Compound LiX [Mn1.96 Li0.04] O4 (X=0.2,0.6,0.8,1.0 ): How A Classical System Can Mimic Quantum Critical Scaling, 2018 Missouri University of Science and Technology

#### Magnetic Excitations In The Spinel Compound LiX [Mn1.96 Li0.04] O4 (X=0.2,0.6,0.8,1.0 ): How A Classical System Can Mimic Quantum Critical Scaling, Thomas Heitmann, Alexander Schmets, John Gaddy, Jagat Lamsal, Marcus Petrovic, Thomas Vojta, Wouter Montfrooij

*Thomas Vojta*

We present neutron-scattering results on the magnetic excitations in the spinel compounds Lix [Mn1.96 Li0.04] O4 (x=0.2,0.6,0.8,1.0). We show that the dominant excitations below T~70K are determined by Mn ions located in clusters, and that these excitations mimic the dynamic scaling found in quantum critical systems that also harbor magnetic clusters, such as CeRu0.5 Fe1.5 Ge2. We argue that our results for this classical spinel compound suggest that the unusual response at low temperatures as observed in quantum critical systems that have been driven to criticality through ...

Influence Of Rare Regions On Magnetic Quantum Phase Transitions, 2018 Missouri University of Science and Technology

#### Influence Of Rare Regions On Magnetic Quantum Phase Transitions, Rajesh S. Narayanan, Thomas Vojta, Dietrich Belitz, Theodore R. Kirkpatrick

*Thomas Vojta*

The effects of quenched disorder on the critical properties of itinerant quantum magnets are considered. Particular attention is paid to locally ordered rare regions that are formed in the presence of quenched disorder even when the bulk system is still in the nonmagnetic phase. It is shown that these local moments or instantons destroy the previously found critical fixed point in the case of antiferromagnets. In the case of itinerant ferromagnets, the critical behavior is unaffected by the rare regions due to an effective long-range interaction between the order parameter fluctuations.

Local Versus Nonlocal Order-Parameter Field Theories For Quantum Phase Transitions, 2018 Missouri University of Science and Technology

#### Local Versus Nonlocal Order-Parameter Field Theories For Quantum Phase Transitions, Dietrich Belitz, Theodore R. Kirkpatrick, Thomas Vojta

*Thomas Vojta*

General conditions are formulated that allow us to determine which quantum phase transitions in itinerant electron systems can be described by a local Landau-Ginzburg-Wilson (LGW) theory solely in terms of the order parameter. A crucial question is the degree to which the order parameter fluctuations couple to other soft modes. Three general classes of zero-wave-number order parameters, in the particle-hole spin-singlet and spin-triplet channels and in the particle-particle channel, respectively, are considered. It is shown that the particle-hole spin-singlet class does allow for a local LGW theory, while the other two classes do not. The implications of this result for ...

First Order Transitions And Multicritical Points In Weak Itinerant Ferromagnets, 2018 Missouri University of Science and Technology

#### First Order Transitions And Multicritical Points In Weak Itinerant Ferromagnets, Dietrich Belitz, Theodore R. Kirkpatrick, Thomas Vojta

*Thomas Vojta*

It is shown that the phase transition in low-Tc clean itinerant ferromagnets is generically of first order, due to correlation effects that lead to a nonanalytic term in the free energy. A tricritical point separates the line of first order transitions from Heisenberg critical behavior at higher temperatures. Sufficiently strong quenched disorder suppresses the first order transition via the appearance of a critical end point. A semiquantitative discussion is given in terms of recent experiments on MnSi, and predictions for other experiments are made.

Generalization Of The Schwartz-Soffer Inequality For Correlated Random Fields, 2018 Missouri University of Science and Technology

#### Generalization Of The Schwartz-Soffer Inequality For Correlated Random Fields, Thomas Vojta, Michael Schreiber

*Thomas Vojta*

We investigate the influence of spatial correlations between the values of the random field on the critical behavior of random-field lattice models and derive a generalized version of the Schwartz-Soffer inequality for the averages of the susceptibility and its disconnected part. At the critical point this leads to a modification of the Schwartz-Soffer exponent inequality for the critical exponents η and η- describing the divergences of the susceptibility and its disconnected part, respectively. It now reads η- ≤ 2η-2y where 2y describes the divergence of the random-field correlation function in Fourier space. As an example we exactly calculate the susceptibility and ...

Generalized Contact Process With Two Symmetric Absorbing States In Two Dimensions, 2018 Missouri University of Science and Technology

#### Generalized Contact Process With Two Symmetric Absorbing States In Two Dimensions, Man Young Lee, Thomas Vojta

*Thomas Vojta*

We explore the two-dimensional generalized contact process with two absorbing states by means of large-scale Monte-Carlo simulations. In part of the phase diagram, an infinitesimal creation rate of active sites between inactive domains is sufficient to take the system from the inactive phase to the active phase. The system, therefore, displays two different nonequilibrium phase transitions. The critical behavior of the generic transition is compatible with the generalized voter universality class, implying that the symmetry-breaking and absorbing transitions coincide. In contrast, the transition at zero domain-boundary activation rate is not critical.

Evidence For Power-Law Griffiths Singularities In A Layered Heisenberg Magnet, 2018 Missouri University of Science and Technology

#### Evidence For Power-Law Griffiths Singularities In A Layered Heisenberg Magnet, Fawaz Hrahsheh, Hatem Barghathi, Priyanka Mohan, Rajesh Narayanan, Thomas Vojta

*Thomas Vojta*

We study the ferromagnetic phase transition in a randomly layered Heisenberg model. A recent strong-disorder renormalization group approach [Phys. Rev. B 81, 144407 (2010)] predicted that the critical point in this system is of exotic infinite-randomness type and is accompanied by strong power-law Griffiths singularities. Here, we report results of Monte-Carlo simulations that provide numerical evidence in support of these predictions. Specifically, we investigate the finite-size scaling behavior of the magnetic susceptibility which is characterized by a non-universal power-law divergence in the Griffiths phase. In addition, we calculate the time autocorrelation function of the spins. It features a very slow ...

Disorder Promotes Ferromagnetism: Rounding Of The Quantum Phase Transition In Sr1-XCaXRuo3, 2018 Missouri University of Science and Technology

#### Disorder Promotes Ferromagnetism: Rounding Of The Quantum Phase Transition In Sr1-XCaXRuo3, Laszlo Demko, Sandor Bordacs, Thomas Vojta, David Nozadze, Fawaz Hrahsheh, Christopher Svoboda, Balazs Dora, Hiroyuki Yamada, Masashi Kawasaki, Yoshinori Tokura, Istvan Kezsmarki

*Thomas Vojta*

The subtle interplay of randomness and quantum fluctuations at low temperatures gives rise to a plethora of unconventional phenomena in systems ranging from quantum magnets and correlated electron materials to ultracold atomic gases. Particularly strong disorder effects have been predicted to occur at zero-temperature quantum phase transitions. Here, we demonstrate that the composition-driven ferromagnetic-to-paramagnetic quantum phase transition in Sr1-xCaxRuO3 is completely destroyed by the disorder introduced via the different ionic radii of the randomly distributed Sr and Ca ions. Using a magneto-optical technique, we map the magnetic phase diagram in the composition-temperature space. We find that the ferromagnetic phase is ...

Disordered Bosons In One Dimension: From Weak- To Strong-Randomness Criticality, 2018 Missouri University of Science and Technology

#### Disordered Bosons In One Dimension: From Weak- To Strong-Randomness Criticality, Fawaz Hrahsheh, Thomas Vojta

*Thomas Vojta*

We investigate the superfluid-insulator quantum phase transition of one-dimensional bosons with off-diagonal disorder by means of large-scale Monte Carlo simulations. For weak disorder, we find the transition to be in the same universality class as the superfluid-Mott insulator transition of the clean system. The nature of the transition changes for stronger disorder. Beyond a critical disorder strength, we find nonuniversal, disorder-dependent critical behavior. We compare our results to recent perturbative and strong-disorder renormalization group predictions. We also discuss experimental implications as well as extensions of our results to other systems.

Dynamical Conductivity At The Dirty Superconductor-Metal Quantum Phase Transition, 2018 Missouri University of Science and Technology

#### Dynamical Conductivity At The Dirty Superconductor-Metal Quantum Phase Transition, Adrian Del Maestro, Bernd Rosenow, Jose A. Hoyos, Thomas Vojta

*Thomas Vojta*

We study the transport properties of ultrathin disordered nanowires in the neighborhood of the superconductor-metal quantum phase transition. To this end we combine numerical calculations with analytical strong-disorder renormalization group results. The quantum critical conductivity at zero temperature diverges logarithmically as a function of frequency. In the metallic phase, it obeys activated scaling associated with an infinite-randomness quantum critical point. We extend the scaling theory to higher dimensions and discuss implications for experiments.

Effect Of Rare Locally Ordered Regions On A Disordered Itinerant Quantum Antiferromagnet With Cubic Anisotropy, 2018 Missouri University of Science and Technology

#### Effect Of Rare Locally Ordered Regions On A Disordered Itinerant Quantum Antiferromagnet With Cubic Anisotropy, Rajesh S. Narayanan, Thomas Vojta

*Thomas Vojta*

We study the quantum phase transition of an itinerant antiferromagnet with cubic anisotropy in the presence of quenched disorder, paying particular attention to the locally ordered spatial regions that form in the Griffiths region. We derive an effective action where these rare regions are described in terms of static annealed disorder. A one-loop renormalization-group analysis of the effective action shows that for order-parameter dimensions p<4, the rare regions destroy the conventional critical behavior, and the renormalized disorder flows to infinity. For order-parameter dimensions p>4, the critical behavior is not influenced by the rare regions; it is described by the conventional dirty cubic fixed point. We also discuss the influence of the rare regions on the fluctuation-driven first-order transition ...

Do Interactions Increase Or Reduce The Conductance Of Disordered Electrons? It Depends!, 2018 Missouri University of Science and Technology

#### Do Interactions Increase Or Reduce The Conductance Of Disordered Electrons? It Depends!, Thomas Vojta, Frank Epperlein, Michael Schreiber

*Thomas Vojta*

We investigate the influence of electron-electron interactions on the conductance of two-dimensional disordered spinless electrons. We present an efficient numerical method based on diagonalization in a truncated basis of Hartree-Fock states to determine with high accuracy the low-energy properties in the entire parameter space. We find that weak interactions increase the dc conductance in the strongly localized regime while they decrease the dc conductance for weak disorder. Strong interactions always decrease the conductance. We also study the localization of single-particle excitations at the Fermi energy which turns out to be only weakly influenced by the interactions.

Disorder-Induced Rounding Of Certain Quantum Phase Transitions, 2018 Missouri University of Science and Technology

#### Disorder-Induced Rounding Of Certain Quantum Phase Transitions, Thomas Vojta

*Thomas Vojta*

We study the influence of quenched disorder on quantum phase transitions in systems with overdamped dynamics. For Ising order-parameter symmetry disorder destroys the sharp phase transition by rounding because a static order parameter can develop on rare spatial regions. This leads to an exponential dependence of the order parameter on the coupling constant. At finite temperatures the static order on the rare regions is destroyed. This restores the phase transition and leads to a double exponential relation between critical temperature and coupling strength. We discuss the behavior based on Lifshitz-tail arguments and illustrate the results by simulations of a model ...

Dissipation Effects In Random Transverse-Field Ising Chains, 2018 Missouri University of Science and Technology

#### Dissipation Effects In Random Transverse-Field Ising Chains, Jose A. Hoyos, Thomas Vojta

*Thomas Vojta*

We study the effects of Ohmic, super-Ohmic, and sub-Ohmic dissipation on the zero-temperature quantum phase transition in the random transverse-field Ising chain by means of an (asymptotically exact) analytical strong-disorder renormalization-group approach. We find that Ohmic damping destabilizes the infinite-randomness critical point and the associated quantum Griffiths singularities of the dissipationless system. The quantum dynamics of large magnetic clusters freezes completely, which destroys the sharp phase transition by smearing. The effects of sub-Ohmic dissipation are similar and also lead to a smeared transition. In contrast, super-Ohmic damping is an irrelevant perturbation; the critical behavior is thus identical to that of ...

Critical Behavior Of Disordered Quantum Magnets: The Relevance Of Rare Regions, 2018 Missouri University of Science and Technology

#### Critical Behavior Of Disordered Quantum Magnets: The Relevance Of Rare Regions, Rajesh S. Narayanan, Thomas Vojta, Dietrich Belitz, Theodore R. Kirkpatrick

*Thomas Vojta*

The effects of quenched disorder on the critical properties of itinerant quantum antiferromagnets and ferromagnets are considered. Particular attention is paid to locally ordered spatial regions that are formed in the presence of quenched disorder even when the bulk system is still in the paramagnetic phase. These rare regions or local moments are reflected in the existence of spatially inhomogeneous saddle points of the Landau-Ginzburg-Wilson functional. We derive an effective theory that takes into account small fluctuations around all of these saddle points. The resulting free energy functional contains a new term in addition to those obtained within the conventional ...