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The chiral anomaly is a fundamental quantum mechanical phenomenon which is of great importance to both particle physics and condensed matter physics alike. In the context of QED it manifests as the breaking of chiral symmetry in the presence of electromagnetic fields. It is also known that anomalous chiral symmetry breaking can occur through interactions alone, as is the case for interacting one dimensional systems. In this paper we investigate the interplay between these two modes of anomalous chiral symmetry breaking in the context of interacting Weyl semimetals. Using Fujikawas path integral method we show that the chiral charge continuity equation is modified by the presence of interactions which can be viewed as including the effect of the electric and magnetic fields generated by the interacting quantum matter. This can be understood further using dimensional reduction and a Luttinger liquid description of the lowest Landau level. These effects manifest themselves in the non-linear response of the system. In particular we find an interaction dependent density response due to a change in the magnetic field as well as a contribution to the non-equilibrium and inhomogeneous anomalous Hall response while preserving its equilibrium value.
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We consider the role of coordinate dependent tetrads (Fermi velocities), momentum space geometry, and torsional Landau levels (LLs) in condensed matter systems with low-energy Weyl quasiparticles. In contrast to their relativistic counterparts, they arise at finite momenta and an explicit cutoff to the linear spectrum. Via the universal coupling of tetrads to momentum, they experience geometric chiral and axial anomalies with gravitational character. More precisely, at low-energy, the fermions experience background fields corresponding to emergent anisotropic Riemann-Cartan and Newton-Cartan spacetimes, depending on the form of the low-energy dispersion. On these backgrounds, we show how torsion and the Nieh-Yan (NY) anomaly appear in condensed matter Weyl systems with a ultraviolet (UV) parameter with dimensions of momentum. The torsional NY anomaly arises in simplest terms from the spectral flow of torsional LLs coupled to the nodes at finite momenta and the linear approximation with a cutoff. We carefully review the torsional anomaly and spectral flow for relativistic fermions at zero momentum and contrast this with the spectral flow, non-zero torsional anomaly and the appearance the dimensionful UV-cutoff parameter in condensed matter systems at finite momentum. We apply this to chiral transport anomalies sensitive to the emergent tetrads in non-homogenous chiral superconductors, superfluids and Weyl semimetals under elastic strain. This leads to the suppression of anomalous density at nodes from geometry, as compared to (pseudo)gauge fields. We also briefly discuss the role torsion in anomalous thermal transport for non-relativistic Weyl fermions, which arises via Luttingers fictitious gravitational field corresponding to thermal gradients.
In this Colloquium recent advances in the field of quantum heat transport are reviewed. This topic has been investigated theoretically for several decades, but only during the past twenty years have experiments on various mesoscopic systems become feasible. A summary of the theoretical basis for describing heat transport in one-dimensional channels is first provided. Then the main experimental investigations of quantized heat conductance due to phonons, photons, electrons, and anyons in such channels are presented. These experiments are important for understanding the fundamental processes that underly the concept of a heat conductance quantum for a single channel. Then an illustration on how one can control the quantum heat transport by means of electric and magnetic fields, and how such tunable heat currents can be useful in devices is given. This lays the basis for realizing various thermal device components such as quantum heat valves, rectifiers, heat engines, refrigerators, and calorimeters. Also of interest are fluctuations of quantum heat currents, both for fundamental reasons and for optimizing the most sensitive thermal detectors; at the end of the review the status of research on this intriguing topic is given.
Electrons in condensed matter have internal degrees of freedom, such as charge, spin and orbital, leading to various forms of ordered states through phase transitions. However, in individual materials, a charge/spin/orbital ordered state of the lowest temperature is normally uniquely determined in terms of the lowest-energy state, i.e., the ground state. Here, we summarize recent results showing that under rapid cooling, this principle does not necessarily hold, and thus, the cooling rate is a control parameter of the lowest-temperature state beyond the framework of the thermo-equilibrium phase diagram. Although the cooling rate utilized in low-temperature experiments is typically 2*10^-3 - 4*10^-1 K/s, the use of optical/electronic pulses facilitate rapid cooling, such as 10^2-10^3 K/s. Such an unconventionally high cooling rate allows some systems to kinetically avoid a first-order phase transition, resulting in a quenched charge/spin state that differs from the ground state. We also demonstrate that quenched states can be exploited as a non-volatile state variable when designing phase-change memory functions. The present findings suggest that rapid cooling is useful for exploring and controlling the metastable electronic/magnetic state that is potentially hidden behind the ground state.
In this review, we describe the potentialities offered by the nuclear magnetic resonance (NMR) technique to explore at a microscopic level new quantum states of condensed matter induced by high magnetic fields. We focus on experiments realised in resistive (up to 34~T) or hybrid (up to 45~T) magnets, which open a large access to these quantum phase transitions. After an introduction on NMR observable, we consider several topics: quantum spin systems (spin-Peierls transition, spin ladders, spin nematic phases, magnetisation plateaus and Bose-Einstein condensation of triplet excitations), the field-induced charge density wave (CDW) in high $T_c$~superconductors, and exotic superconductivity including the Fulde-Ferrel-Larkin-Ovchinnikov superconducting state and the field-induced superconductivity due to the Jaccarino-Peter mechanism.
Harnessing power-law interactions ($1/r^alpha$) in a large variety of physical systems are increasing. We study the dynamics of chiral spin chains as a possible multi-directional quantum channel. This arises from the nonlinear character of the dispersion with complex quantum interference effects. Using complementary numerically and analytical techniques, we engineer models to transfer quantum states. We illustrate our approach using the long-range XXZ model modulated by Dzyaloshinskii-Moriya (DM) interaction. With exploring non-equilibrium dynamics after a local quantum quench, we identify at fully nonlocal regime (which breaks generalized Lieb-Robinson bounds ) the interplay of interaction range $alpha$ and Dzyaloshinskii-Moriya coupling gives rise to spatially asymmetric spin excitations transport. This could be interesting for quantum information protocols to transfer quantum states and maybe testable with current trapped-ion experiments. We further explore the growth of block entanglement entropy in these systems and the order of magnitude reduction distinguished. A possible effective interaction induces by DM coupling and integrability breaking in these systems is discussed.
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