arXiv subjects

D. Belitz

Publications and source records attributed to D. Belitz.

At least 19 recordsLinked to original sources

arXiv2026

Generic Long-Range Order-Parameter Correlations in Metallic Quantum Magnets

It is shown that in all types of metallic magnets the coupling of the order parameter to the conduction electrons leads to an order-parameter susceptibility that is long-ranged at zero temperature. This is true for all known classes of ferromagnets, and also for antiferromagnets and spin-density wave systems, helimagnets, magnetic nematics, and altermagnets. The consequences for the magnetic quantum phase transition vary between different classes of magnets. In almost all 3-d systems with a homogeneous magnetization, as well as in magnetic nematics and in altermagnets, the long-ranged correlations generically modify the nature of the magnetic quantum phase transition from second order to first order. The only exception are non-centrosymmetric ferromagnets with a strong spin-orbit interaction, where the correlations change the order of the transition in 2-d systems, but not in 3-d ones. In helimagnets, spin-wave systems, and Neel antiferromagnets their effect is even weaker and does not change the order of the transition if the ordering wave number is sufficiently large, except in flat-band systems. In systems with quenched disorder the transition generically is of second order, but the correlations modify the critical behavior. These conclusions are reached by very simple considerations that are based entirely on the single-particle excitations in the nonmagnetic phase and their modifications by a field conjugate to the order parameter, augmented by renormalization-group considerations.

cond-mat.str-el↗

arXiv2026

Comment on "Instability of the ferromagnetic quantum critical point and symmetry of the ferromagnetic ground state in two-dimensional and three-dimensional electron gases with arbitrary spin-orbit splitting"

Metallic quantum ferromagnets in the absence of quenched disorder are known to generically undergo a first-order quantum phase transition, avoiding the quantum critical point that had originally been expected. This is due to soft modes in the underlying Fermi liquid that lead to long-ranged correlations. These correlations in turn yield a nonanalytic dependence of the free energy on the magnetization even at a mean-field level that results in a fluctuation-induced first-order transition. Kirkpatrick and Belitz [Phys. Rev. Lett. {\bf 124}, 147201 (2020)] have pointed out that one notable exception are non-centrosymmetric metals with a strong spin-orbit interaction. In such materials the spin-orbit interaction gives the relevant soft modes a mass, which inhibits the mechanism leading to a first-order transition. Miserev, Loss, and Klinovaja [Phys. Rev. B {\bf 106}, 134417 (2022)] have claimed that this conclusion does not hold if electron-electron interactions in the particle-particle channel, or 2$\kF$ scattering processes, are considered. They concluded that this interaction channel leads to soft modes that are not rendered massive by the spin-orbit interaction and again lead to a first-order quantum phase transition. In this Comment we show that this conclusion is not correct in three-dimensional magnets if the screening of the interaction is properly taken into account.

cond-mat.str-el↗

arXiv2024

Diffusion, Long-Time Tails, and Localization in Classical and Quantum Lorentz Models: A Unifying Hydrodynamic Approach

Long-time tails, or algebraic decay of time-correlation functions, have long been known to exist both in many-body systems and in models of non-interacting particles in the presence of quenched disorder that are often referred to as Lorentz models. In the latter, they have been studied extensively by a wide variety of methods, the best known example being what is known as weak-localization effects in disordered systems of non-interacting electrons. This paper provides a unifying, and very simple, approach to all of these effects. We show that simple modifications of the diffusion equation due to either a random diffusion coefficient, or a random scattering potential, accounts for both the decay exponents and the prefactors of the leading long-time tails in the velocity autocorrelation functions of both classical and quantum Lorentz models.

cond-mat.dis-nn↗

arXiv2024

Fluctuation-Response Relation in Non-Equilibrium Systems and Active Matter

We use dynamic equations to derive a relation between correlation functions and response or relaxation functions in many-body systems. The relation is very general and holds both in equilibrium, when the usual fluctuation-dissipation theorem is valid, and to linear order in an expansion about arbitrary non-equilibrium states, when it is not. We illustrate our results by discussing fluids, both in equilibrium and non-equilibrium states, as well as several active-matter systems.

cond-mat.stat-mech↗

arXiv2024

A Fluctuation-Response Relation as a Probe of Long-Range Correlations in Non-Equilibrium Quantum and Classical Fluids

The absence of a simple fluctuation-dissipation theorem is a major obstacle for studying systems that are not in thermodynamic equilibrium. We show that for a fluid in a non-equilibrium steady state characterized by a constant temperature gradient the commutator correlation functions are still related to response functions; however, the relation is to the bilinear response of products of two observables, rather than to a single linear response function as is the case in equilibrium. This modified fluctuation-response relation holds for both quantum and classical systems. It is both motivated and informed by the long-range correlations that exist in such a steady state and allows for probing them via response experiments. This is of particular interest in quantum fluids, where the direct observation of fluctuations by light scattering would be difficult. In classical fluids it is known that the coupling of the temperature gradient to the diffusive shear velocity leads to correlations of various observables, in particular temperature fluctuations, that do not decay as a function of distance, but rather extend over the entire system. We investigate the nature of these correlations in a fermionic quantum fluid and show that the crucial coupling between the temperature gradient and velocity fluctuations is the same as in the classical case. Accordingly, the nature of the long-ranged correlations in the hydrodynamic regime also is the same. However, as one enters the collisionless regime in the low-temperature limit the nature of the velocity fluctuations changes: they become ballistic rather than diffusive. As a result, correlations of the temperature and other observables are still singular in the long-wavelength limit, but the singularity is weaker than in the hydrodynamic regime.

cond-mat.stat-mech↗

arXiv2023

Fluctuation-dissipation relation in a non-equilibrium quantum fluid

There is no simple fluctuation-dissipation theorem (FDT) for nonequilibrium systems. We show that for a fluid in a nonequilibrium steady state (NESS) characterized by a constant temperature gradient there is a generalized FDT that relates commutator correlation functions to the bilinear response of products of observables. This allows for experimental probes of the long-range correlations in such a system, quantum or classical, via response experiments. We also show that the correlations are not tied to thermal fluctuations but are intrinsic to the NESS and reflect a generalized rigidity.

cond-mat.stat-mech↗

arXiv2023

Velocity-Dependent Forces and Non-Hydrodynamic Initial Conditions in Quantum and Classical Fluids

We consider a fermionic fluid in a non-equilibrium steady state where the fluctuation-dissipation theorem is not valid and fields conjugate to the hydrodynamic variables are explicitly required to determine response functions. We identify velocity-dependent forces in the kinetic equation that are equivalent to such fields. They lead to driving terms in the hydrodynamic equations and to corrections to the hydrodynamic initial conditions.

cond-mat.stat-mech↗

arXiv2022

Thermal Transport and Non-Mechanical Forces in Metals

We discuss contributions to the thermopower in an electron fluid. A simple argument based on Newton's second law with the pressure gradient as the force suggests that the thermopower is given by a thermodynamic derivative, viz., the entropy per particle, rather than being an independent transport coefficient. The resolution is the existence of an entropic force that results from a coupling between the mass current and the heat current in the fluid. We also discuss and clarify some aspects of a recent paper (Phys. Rev. B {\bf 102}, 214306 (2020)) that provided a method for exactly solving electronic transport equations in the low-temperature limit.

cond-mat.stat-mech↗

arXiv2022

Soft modes in Fermi liquids at arbitrary temperatures

We use kinetic-theory methods to analyze Landau Fermi-liquid theory, and in particular to investigate the number and nature of soft modes in Fermi liquids, both in the hydrodynamic and the collisionless regimes. In the hydrodynamic regime we show that Fermi-liquid theory is consistent with Navier-Stokes hydrodynamics at all temperatures. The soft modes are the ones familiar from classical hydrodynamics that are controlled by the five conservation laws; namely, two first-sound modes, two shear diffusion modes, and one heat diffusion mode. These modes have a particle-like spectrum and are soft, or scale invariant, at all temperatures. In the collisionless regime we show that the entire single-particle distribution function is soft with a continuous part of the spectrum. This continuous soft mode, which is well known but often not emphasized, has important physical consequences, e.g., for certain quantum phase transitions. In addition, there are the well known soft zero-sound excitations that describe angular fluctuations of the Fermi surface; their spectra are particle-like. They are unrelated to conservation laws, acquire a mass at any nonzero temperature, and their number depends on the strength of the quasiparticle interaction. We also discuss the fates of these two families of soft modes as the temperature changes. With increasing temperature the size of the collisionless regime shrinks, the damping of the modes grows, and eventually all of the collisionless modes become overdamped. In their stead the five hydrodynamic modes appear in the hydrodynamic regime at asymptotically low frequencies. The two families of soft modes are unrelated and have very different physical origins.In charged Fermi liquids the first-sound modes in the hydrodynamic regime and the l=0 zero-sound modes in the collisionless regime get replaced by plasmons, all other modes remain soft.

cond-mat.stat-mech↗

arXiv2022

Fluctuating Quantum Kinetic Theory

We consider a quantum Langevin kinetic equation for a system of fermions. We first derive the Langevin force noise correlation functions in Landau's Fermi-liquid kinetic theory from general considerations. We then use the resulting equation to calculate the equilibrium dynamic structure factor in the collisionless regime at low temperatures. The result is in agreement with the conventional many-body result. We then use the theory to derive both the fluctuating Navier-Stokes equations for a quantum fluid and the fluctuating hydrodynamic equations for fermions in the presence of quenched disorder. We also discuss the modifications needed for the fluctuating hydrodynamic equations to describe an electron fluid with long-ranged interactions, and we prove an H-theorem for the nonlinear Landau kinetic equation.

cond-mat.stat-mech↗

arXiv2021

Rigidity and Superfast Signal Propagation in Fluids and Solids in Non-Equilibrium Steady States

In the 1980s it was theoretically predicted that correlations of various observables in a fluid in a non-equilibrium steady state (NESS) are extraordinarily long-ranged, extending, in a well-defined sense, over the size of the system. This is to be contrasted with correlations in an equilibrium fluid, whose range is typically just a few particle diameters. These NESS correlations were later confirmed by numerous experimental studies. Unlike long-ranged correlations at critical points, these correlations are generic in the sense that they exist for any temperature as long as the system is in a NESS. In equilibrium systems, generic long-ranged correlations are caused by spontaneously broken continuous symmetries and are associated with a generalized rigidity, which in turn leads to a new propagating excitation or mode. For example, in a solid, spatial rigidity leads to transverse sound waves, while in a superfluid, phase rigidity leads to temperature waves known as second sound at finite temperatures, and phonons at zero temperature. More generally, long-ranged spatial correlations imply rigidity irrespective of their physical origin. This implies that a fluid in a NESS should also display a type of rigidity and related anomalous transport behavior. Here we show that this is indeed the case. For the particular case of a simple fluid in a constant temperature gradient, the anomalous transport behavior takes the form of a super-diffusive spread of a constant-pressure temperature perturbation. We also discuss the case of an elastic solid, where we predict a spread that is faster than ballistic.

cond-mat.stat-mech↗

arXiv2021

Non-Hydrodynamic Initial Conditions are Not Soon Forgotten

Solutions to hydrodynamic equations, which are used for a vast variety of physical problems, are assumed to be specified by boundary conditions and initial conditions on the hydrodynamic variables only. Initial values of other variables are assumed to be irrelevant for a hydrodynamic description. This assumption is not correct because of the existence of long-time-tail effects that are ubiquitous in systems governed by hydrodynamic equations. We illustrate this breakdown of a hydrodynamic description by means of the simple example of diffusion in a disordered electron system.

cond-mat.stat-mech↗

arXiv2020

Exact solution of the Boltzmann equation for low-temperature transport coefficients in metals I: Scattering by phonons, antiferromagnons, and helimagnons

We present a technique for an exact solution of the linearized Boltzmann equation for the electrical and thermal transport coefficients in metals in the low-temperature limit. This renders unnecessary an uncontrolled approximation that has been used in all previous solutions of the integral equations for the transport coefficients. Applications include electron-phonon scattering in nonmagnetic metals, as well as the magnon contribution to the electrical and thermal conductivities, and to the thermopower, in metallic ferromagnets, antiferromagnets, and helimagnets. In this paper, the first of a pair, we set up the technique and apply it to the scattering of electrons by phonons, antiferromagnons, and helimagnons. We show that the Bloch $T^5$ law for the electrical resistivity, the $T^2$ law for the thermal resistivity, and the $T$ law for the thermopower due to phonon and antiferromagnon scattering are exact, and determine the prefactors exactly. The corresponding exact results for helimagnons are $T^{5/2}$, $T^{1/2}$, and $T$, respectively. In a second paper we will consider the scattering by ferromagnons.

cond-mat.stat-mech↗

arXiv2020

Exact solution of the Boltzmann equation for low-temperature transport coefficients in metals II: Scattering by ferromagnons

In a previous paper (Paper I) we developed a technique for exactly solving the linearized Boltzmann equation for the electrical and thermal transport coefficients in metals in the low-temperature limit. Here we adapt this technique to determine the magnon contribution to the electrical and thermal conductivities, and to the thermopower, in metallic ferromagnets. For the electrical resistivity $ρ$ at asymptotically low temperatures we find $ρ\propto \exp{(-T_{\rm min}/T)}$, with $T_{\rm min}$ an energy scale that results from the exchange gap and a temperature independent prefactor of the exponential. The corresponding result for the heat conductivity is $σ_h \propto T^3\,\exp{(T_{\rm min}/T)}$, and thermopower is $S \propto T$. All of these results are exact, including the prefactors.

cond-mat.stat-mech↗

arXiv2020

Ferromagnetic Quantum Critical Point in Non-Centrosymmetric Systems

Ferromagnetic quantum criticality in clean metals has proven elusive due to fermionic soft modes that drive the transition first order. We show that non-centrosymmetric metals with a strong spin-orbit interaction provide a promising class of materials for realizing a ferromagnetic quantum critical point in clean systems. The spin-orbit interaction renders massive the soft modes that interfere with quantum criticality in most materials, while the absence of spatial inversion symmetry precludes the existence of new classes of soft modes that could have the same effect.

cond-mat.str-el↗

arXiv2020

Rigorous results for the electrical conductivity due to electron-phonon scattering

We present a rigorous solution of the Boltzmann equation for the electron-phonon scattering problem in three spatial dimensions in the limit of low temperatures. The different temperature scaling of the various scattering rates turns the temperature into a control parameter that is not available in classical kinetic theory and allows for a rigorous proof of Bloch's $T^5$ law. The relation between the Boltzmann equation and the Kubo formula is also discussed, as well as implications for the scattering of electrons by excitations other than phonons.

math-ph↗

arXiv2019

Magnetic Quantum Phase Transitions in a Clean Dirac Metal

We consider clean Dirac metals where the linear band crossing is caused by a strong spin-orbit interaction, and study the quantum phase transitions from the paramagnetic phase to various magnetic phases, including homogeneous ferromagnets, ferrimagnets, canted ferromagnets, and magnetic nematics. We show that in all of these cases the coupling of fermionic soft modes to the order parameter generically renders the quantum phase transition first order, with certain gapless Dirac systems providing a possible exception. These results are surprising since a strong spin-orbit scattering suppresses the mechanism that causes the first order transition in ordinary metals. The important role of chirality in generating a new mechanism for a first-order transition is stressed.

cond-mat.str-el↗

arXiv2019

Quantum Ferromagnetic Transition in Clean Dirac Metals

The ferromagnetic quantum phase transition in clean metals with a negligible spin-orbit interaction is known to be first order due to a coupling of the magnetization to soft fermionic particle-hole excitations. A spin-orbit interaction gives these excitations a mass, suggesting the existence of a ferromagnetic quantum critical point in metals with a strong spin-orbit interaction. We show that this expectation is not borne out in a large class of materials with a Dirac spectrum, since the chirality degree of freedom leads to new soft modes that again render the transition first order.

cond-mat.str-el↗