Environmental interaction is a fundamental consideration in any controlled quantum system. While interaction with a dissipative bath can lead to decoherence, it can also provide desirable emergent effects including induced spin-spin correlations. In
this paper we show that under quite general conditions, a dissipative bosonic bath can induce a long-range ordered phase, without the inclusion of any additional direct spin-spin couplings. Through a quantum-to-classical mapping and classical Monte Carlo simulation, we investigate the $T=0$ quantum phase transition of an Ising chain embedded in a bosonic bath with Ohmic dissipation. We show that the quantum critical point is continuous, Lorentz invariant with a dynamical critical exponent $z=1.07(9)$, has correlation length exponent $ u=0.80(5)$, and anomalous exponent $eta=1.02(6)$, thus the universality class distinct from the previously studied limiting cases. The implications of our results on experiments in ultracold atomic mixtures and qubit chains in dissipative environments are discussed.
We develop a theory for manipulating the effective band structure of interacting helical edge states realized on the boundary of two-dimensional time-reversal symmetric topological insulators. For sufficiently strong interaction, an interacting edge
band gap develops, spontaneously breaking time-reversal symmetry on the edge. The resulting spin texture, as well as the energy of the the time-reversal breaking gaps, can be tuned by an external moire potential (i.e., a superlattice potential). Remarkably, we establish that by tuning the strength and period of the potential, the interacting gaps can be fully suppressed and interacting Dirac points re-emerge. In addition, nearly flat bands can be created by the moire potential with a sufficiently long period. Our theory provides a novel way to enhance the coherence length of interacting helical edges by suppressing the interacting gap. The implications of this finding for ongoing experiments on helical edge states is discussed.
Disorder in Weyl semimetals and superconductors is surprisingly subtle, attracting attention and competing theories in recent years. In this brief review, we discuss the current theoretical understanding of the effects of short-ranged, quenched disor
der on the low energy-properties of three-dimensional, topological Weyl semimetals and superconductors. We focus on the role of non-perturbative rare region effects on destabilizing the semimetal phase and rounding the expected semimetal-to-diffusive metal transition into a cross over. Furthermore, the consequences of disorder on the resulting nature of excitations, transport, and topology are reviewed. New results on a bipartite random hopping model are presented that confirm previous results in a $p+ip$ Weyl superconductor, demonstrating that particle-hole symmetry is insufficient to help stabilize the Weyl semimetal phase in the presence of disorder. The nature of the avoided transition in a model for a single Weyl cone in the continuum is discussed. We close with a discussion of open questions and future directions.
Motivated by the recent achievements in the realization of strongly correlated and topological phases in twisted van der Waals heterostructures, we study the low-energy properties of a twisted bilayer of nodal superconductors. It is demonstrated that
the spectrum of the superconducting Dirac quasiparticles close to the gap nodes is strongly renormalized by twisting and can be controlled with magnetic fields, current, or interlayer voltage. In particular, the application of an interlayer current transforms the system into a topological superconductor, opening a topological gap and resulting in a quantized thermal Hall effect with gapless, neutral edge modes. Close to the magic angle, where the Dirac velocity of the quasiparticles is found to vanish, a correlated superconducting state breaking time-reversal symmetry is shown to emerge. Estimates for a number of superconducting materials, such as cuprate, heavy fermion, and organic nodal superconductors, show that twisted bilayers of nodal superconductors can be readily realized with current experimental techniques.
Twisting van der Waals heterostructures to induce correlated many-body states provides a novel tuning mechanism in solid-state physics. In this work, we theoretically investigate the fate of the surface Dirac cone of a three-dimensional topological i
nsulator subject to a superlattice potential. Using a combination of diagrammatic perturbation theory, lattice model simulations, and ab initio calculations we elucidate the unique aspects of twisting a single Dirac cone with an induced moire potential and the role of the bulk topology on the reconstructed surface band structure. We report a dramatic renormalization of the surface Dirac cone velocity as well as demonstrate a topological obstruction to the formation of isolated minibands. Due to the topological nature of the bulk, surface band gaps cannot open; instead, additional satellite Dirac cones emerge, which can be highly anisotropic and made quite flat. We discuss the implications of our findings for future experiments.
We theoretically study correlations present deep in the spectrum of many-body-localized systems. An exact analytical expression for the spectral form factor of Poisson spectra can be obtained and is shown to agree well with numerical results on two m
odels exhibiting many-body-localization: a disordered quantum spin chain and a phenomenological $l$-bit model based on the existence of local integrals of motion. We also identify a universal regime that is insensitive to the global density of states as well as spectral edge effects.
The effects of downfolding a Brillouin zone can open gaps and quench the kinetic energy by flattening bands. Quasiperiodic systems are extreme examples of this process, which leads to new phases and critical eigenstates. We analytically and numerical
ly investigate these effects in a two dimensional topological insulator with a quasiperiodic potential and discover a complex phase diagram. We study the nature of the resulting eigenstate quantum phase transitions; a quasiperiodic potential can make a trivial insulator topological and induce topological insulator-to-metal phase transitions through a unique universality class distinct from random systems. This wealth of critical behavior occurs concomitantly with the quenching of the kinetic energy, resulting in flat topological bands that could serve as a platform to realize the fractional quantum Hall effect without a magnetic field.
Motivated by recent experiments on magnetically frustrated heavy fermion metals, we theoretically study the phase diagram of the Kondo lattice model with a nonmagnetic valence bond solid ground state on a ladder. A similar physical setting may be nat
urally occurring in YbAl$_3$C$_3$, CeAgBi$_2$, and TmB$_4$ compounds. In the insulating limit, the application of a magnetic field drives a quantum phase transition to an easy-plane antiferromagnet, which is described by a Bose-Einstein condensation of magnons. Using a combination of field theoretical techniques and density matrix renormalization group calculations we demonstrate that in one dimension this transition is stable in the presence of a metallic Fermi sea and its universality class in the local magnetic response is unaffected by the itinerant gapless fermions. Moreover, we find that fluctuations about the valence bond solid ground state can mediate an attractive interaction that drives unconventional superconducting correlations. We discuss the extensions of our findings to higher dimensions and argue that, depending on the filling of conduction electrons, the magnon Bose-Einstein condensation transition can remain stable in a metal also in dimensions two and three.
We study the chiral anomaly in disordered Weyl semimetals, where the broken translational symmetry prevents the direct application of Nielsen and Ninomiyas mechanism and disorder is strong enough that quantum effects are important. In the weak disord
er regime, there exist rare regions of the random potential where the disorder strength is locally strong, which gives rise to quasilocalized resonances and their effect on the chiral anomaly is unknown. We numerically show that these resonant states do not affect the chiral anomaly only in the case of a single Weyl node. At energies away from the Weyl point, or with strong disorder where one is deep in the diffusive regime, the chiral Landau level itself is not well defined and the semiclassical treatment is not justified. In this limit, we analytically use the supersymmetry method and find that the Chern-Simons term in the effective action which is not present in nontopological systems gives rise to a nonzero average level velocity which implies chiral charge pumping. We numerically establish that the nonzero average level velocity serves as an indicator of the chiral anomaly in the diffusive limit.
We explore the stability of three-dimensional Weyl and Dirac semimetals subject to quasiperiodic potentials. We present numerical evidence that the semimetal is stable for weak quasiperiodic potentials, despite being unstable for weak random potentia
ls. As the quasiperiodic potential strength increases, the semimetal transitions to a metal, then to an inverted semimetal, and then finally to a metal again. The semimetal and metal are distinguished by the density of states at the Weyl point, as well as by level statistics, transport, and the momentum-space structure of eigenstates near the Weyl point. The critical properties of the transitions in quasiperiodic systems differ from those in random systems: we do not find a clear critical scaling regime in energy; instead, at the quasiperiodic transitions, the density of states appears to jump abruptly (and discontinuously to within our resolution).
