We investigate the effects of quenched randomness on topological quantum phase transitions in strongly interacting two-dimensional systems. We focus first on transitions driven by the condensation of a subset of fractionalized quasiparticles (`anyons') identified with `electric charge' excitations of a phase with intrinsic topological order. All other anyons have nontrivial mutual statistics with the condensed subset and hence become confined at the anyon condensation transition. Using a combination of microscopically exact duality transformations and asymptotically exact real-space renormalization group techniques applied to these two-dimensional disordered gauge theories, we argue that the resulting critical scaling behavior is `superuniversal' across a wide range of such condensation transitions, and is controlled by the same infinite-randomness fixed point as that of the 2D random transverse-field Ising model. We validate this claim using large-scale quantum Monte Carlo simulations that allow us to extract zero-temperature critical exponents and correlation functions in (2+1)D disordered interacting systems. We discuss generalizations of these results to a large class of ground-state and excited-state topological transitions in systems with intrinsic topological order as well as those where topological order is either protected or enriched by global symmetries. When the underlying topological order and the symmetry group are Abelian, our results provide prototypes for topological phase transitions between distinct many-body localized phases.
Pursuing complementary field-theoretic and numerical methods, we here paint the global phase diagram of a three-dimensional dirty Weyl system. The generalized Harris criterion, augmented by a perturbative renormalization-group (RG) analysis shows that weak disorder is an irrelevant perturbation at the Weyl semimetal(WSM)-insulator quantum critical point (QCP). But, a metallic phase sets in through a quantum phase transition (QPT) at strong disorder across a multicritical point (MCP). The field theoretic predictions for the correlation length exponent $ν=2$ and dynamic scaling exponent $z=5/4$ …
We use the Lindblad equation method to investigate the onset of a mobility edge and the topological phase transition in the disordered SSH chain connected to two external baths in the large bias limit. From the scaling properties of the nonequilibrium stationary current flowing across the system, we recover the localization/delocalization in the disordered chain. To probe the topological phase transition in the presence of disorder, we use the even-odd differential occupancy as a mean to discriminate topologically trivial from topologically nontrival phases in the out-of-equilibirum system. Ev…
We study one-dimensional disordered fermions that either undergo metal-insulator transitions or topological phase transitions to become trivial Anderson insulators. We focus on using entanglement to elucidate how the spatial, momentum, and internal degrees of freedom of fermions are affected by the presence of disorder in such cases. We develop entanglement tools that reveal the existence of metallic states in the presence of disorder and further show clear signatures of the corresponding localization transition even in the presence of interactions. In systems where the internal degrees of fre…
When translational symmetry is broken by bulk disorder, the topological nature of states in topological crystalline systems may change depending on the type of disorder that is applied. In this work, we characterize the phases of a one-dimensional (1D) chain with inversion and chiral symmetries, where every disorder configuration is inversion-symmetric. By using a basis-independent formulation for the inversion topological invariant, chiral winding number, and bulk polarization, we are able to construct phase diagrams for these quantities when disorder is present. We show that unlike the chira…
Calculation of topological invariants for crystalline systems is well understood in reciprocal space, allowing for the topological classification of a wide spectrum of materials. In this work, we present a new technique based on the entanglement spectrum, which can be used to identify the hidden topology of systems without translational invariance. By training a neural network to distinguish between trivial and topological phases using the entanglement spectrum obtained from crystalline or weakly disordered phases, we can predict the topological phase diagram for generic disordered systems. Th…
Boundary obstructed topological insulators are an unusual class of higher-order topological insulators with topological characteristics determined by the so-called Wannier bands. Boundary obstructed phases can harbor hinge/corner modes, but these modes can often be destabilized by a phase transition on the boundary instead of the bulk. While there has been much work on the stability of topological insulators in the presence disorder, the topology of a disordered Wannier band, and disorder-induced Wannier transitions have not been extensively studied. In this work, we focus on the simplest exam…
Topological phases of matter are considered the bedrock of novel quantum materials as well as ideal candidates for quantum computers that possess robustness at the physical level. The robustness of the topological phase at finite temperature or away from equilibrium is therefore a very desirable feature. Disorder can improve the lifetime of the encoded topological qubits. Here we tackle the problem of the survival of the topological phase as detected by topological entropy, after a sudden quantum quench. We introduce a method to study analytically the time evolution of the system after a quant…
Interacting disordered zigzag graphene nanoribbons have fractional charges, are quasi-one-dimensional, and display an exponentially small gap. Our numerical computations showed that the topological entanglement entropy of these systems has a small finite but universal value, independent of the strength of the interaction and the disorder. The result that was obtained for the topological entanglement entropy shows that the disorder-free phase is critical and becomes unstable in the presence of disorder.
In recent years, tools from quantum information theory have become indispensable in characterizing many-body systems. In this work, we employ measures of entanglement to study the interplay between disorder and the topological phase in 1D systems of the Kitaev type, which can host Majorana end modes at their edges. We find that the entanglement entropy may actually increase as a result of disorder, and identify the origin of this behavior in the appearance of an infinite-disorder critical point. We also employ the entanglement spectrum to accurately determine the phase diagram of the system, a…
Robustness to disorder - the defining property of any topological state - has been mostly tested in low-disorder translationally-invariant materials systems where the protecting underlying symmetry, such as time reversal, is preserved. The ultimate disorder limits to topological protection are still unknown, however, a number of theories predict that even in the amorphous state a quantized conductance might yet reemerge. Here we report a directly detected robust spin response in structurally disordered thin films of the topological material Sb2Te3 free of extrinsic magnetic dopants, which we c…
Using a combination of the mean-field Bogoliubov deGennes (BdG) approach and the Density Matrix Renormalization Group (DMRG) method, we discover first order topological transitions between topological superconducting and trivial insulating phases in a sawtooth lattice of inter-site attractive fermions. Topological characterization of different phases is achieved in terms of winding numbers, Majorana edge modes and entanglement spectra. By studying the effect of disorder on the first order topological phase transitions, we establish the disorder-induced topological phase coexistence as a mechan…
Three-dimensional topological insulators feature Dirac-like surface states which are topologically protected against the influence of weak quenched disorder. Here we investigate the effect of surface disorder beyond the weak-disorder limit using large-scale numerical simulations. We find two qualitatively distinct regimes: Moderate disorder destroys the Dirac cone and induces diffusive metallic behavior at the surface. Even more remarkably, for strong surface disorder a Dirac cone reappears, as new weakly disordered "surface" states emerge in the sample beneath the disordered surface layer, wh…
We analyze the effect of disorder on the weak-coupling instabilities of quadratic band crossing point (QBCP) in two-dimensional Fermi systems, which, in the clean limit, display interaction- driven topological insulating phases. In the framework of a renormalization group procedure, which treats fermionic interactions and disorder on the same footing, we test all possible instabilities and identify the corresponding ordered phases in the presence of disorder for both single-valley and two-valley QBCP systems. We find that disorder generally suppresses the critical temperature at which the inte…
We study the combined effect of interactions and disorder on topological order in one dimension. To this end we consider a generalized Kitaev chain including fermion-fermion interactions and disorder in the chemical potential. We determine the phase diagram by performing density-matrix renormalization group calculations on the corresponding spin-1/2 chain. We find that moderate disorder or repulsive interactions individually stabilize the topological order, which remains valid for their combined effect. However, both repulsive and attractive interactions lead to a suppression of the topologica…
We focus on inducing topological state from regular, or irregular scattering in (i) p-wave superconducting wires and (ii) Rashba wires proximity coupled to an s-wave superconductor. We find that contrary to common expectations the topological properties of both systems are fundamentally different: In p-wave wires, disorder generally has a detrimental effect on the topological order and the topological state is destroyed beyond a critical disorder strength. In contrast, in Rashba wires, which are relevant for recent experiments, disorder can {\it induce} topological order, reducing the need for…
In recent experiments, time-dependent periodic fields are used to create exotic topological phases of matter with potential applications ranging from quantum transport to quantum computing. These nonequilibrium states, at high driving frequencies, exhibit the quintessential robustness against local disorder similar to equilibrium topological phases. However, proving the existence of such topological phases in a general setting is an open problem. We propose a universal effective theory that leverages on modern free probability theory and ideas in random matrices to analytically predict the exi…
Texas Center for Superconductivity and Department of Physics, University of Houston（休斯顿大学物理系超导电性中心）；Department of Physics and Astronomy, Rice University（莱斯大学物理与天文学系）；Rice Center for Quantum Materials, Rice University（莱斯大学量子材料中心）
We study the Majorana surface states of higher-spin topological superconductors (TSCs) that could be realized in ultracold atomic systems or doped semimetals with spin-orbit coupling. As a paradigmatic example, we consider a model with p-wave pairing of spin-3/2 fermions that generalizes ${}^3\text{He-}B$. This model has coexisting linear and cubic dispersing Majorana surface bands. We show that these are unstable to interactions, which can generate a spontaneous surface thermal quantum Hall effect (TQHE). By contrast, nonmagnetic quenched disorder induces a surface conformal field theory (CFT…
Searching for spin liquids on the honeycomb J1-J2 Heisenberg model has been attracting great attention in the past decade. In this Paper we investigate the topological properties of the J1-J2 Heisenberg model by introducing nearest-neighbour and next-nearest-neighbour bond parameters. We find that there exist two topologically different phases in the spin disordered regime 0.2<J2/J1<0.5: for J2/J1<0.32, the system is a zero-flux spin liquid which is topological trivial and gapless; for J2/J1>0.32, it is a pi-flux chiral spin liquid, which is topological nontrivial and gapped. These results sug…
Using exact diagonalization and quantum Monte Carlo calculations we investigate the effects of disorder on the phase diagram of both non-interacting and interacting models of two-dimensional topological insulators. In the fermion sign problem-free interacting models we study, electron-electron interactions are described by an on-site repulsive Hubbard interaction and disorder is included via the one-body hopping operators. In both the non-interacting and interacting models we make use of recent advances in highly accurate real-space numerical evaluation of topological invariants to compute pha…
The robustness against local perturbations, as long as the symmetry of the system is preserved, is a distinctive feature of topological quantum states. Magnetic impurities and defects break time-reversal invariance and, consequently, time-reversal invariant (TRI) topological superconductors are fragile against this type of disorder. Non-magnetic impurities, however, preserve time-reversal symmetry and one naively expects a TRI topological superconductor to persist in the presence of non-magnetic impurities. In this work, we study the effect of non-magnetic disorder on a TRI topological superco…
Topological insulators in three dimensions are characterized by a Z2-valued topological invariant, which consists of a strong index and three weak indices. In the presence of disorder, only the strong index survives. This paper studies the topological invariant in disordered three-dimensional system by viewing it as a super-cell of an infinite periodic system. As an application of this method we show that the strong index becomes non-trivial when strong enough disorder is introduced into a trivial insulator with spin-orbit coupling, realizing a strong topological Anderson insulator. We also nu…
We analyse the topological transition and localization evolution of disordered two dimensional systems with non trivial topology based on bipartite lattices. Chern insulators with broken time reversal symmetry show non standard behavior for disorder realizations selectively distributed on only one of the sublattices. The Chern number survives to a much stronger disorder strength (one order of magnitude higher) than in the equally distributed disordered case and the final state in the strongly disordered case is metallic.
We examine the transport properties of magnetically doped topological insulator (TI) thin films subject to correlated non-magnetic disorder. For the disorder we choose a quasi-periodic potential with a random phase. We restrict the disorder to a central region, which is coupled to two leads in a clean quantum spin Hall insulator (QSHI) state and concentrate on different orientations of the quasi-periodicity in the two-dimensional central region. In the case of a diagonally oriented or purely longitudinal quasi-periodicity we find different topological Anderson insulator (TAI) phases, with a qu…
We study the half-filled Haldane model with Anderson and binary disorder and determine its phase diagram, as a function of the Haldane flux and staggered sub-lattice potential, for increasing disorder strength. We establish that disorder stabilizes topologically nontrivial phases in regions of the phase diagram where the clean limit is topologically trivial. At small disorder strength, our results agree with analytical predictions obtained using a first order self-consistent Born approximation, and extend to the intermediate and large disorder values where this perturbative approach fails. We …
We investigate the robustness of Majorana edge modes under disorder and interactions. We exploit a recently found mapping of the interacting Kitaev chain in the symmetric region ($μ= 0$, $t = Δ$) to free fermions. Extending the exact solution to the disordered case allows us to calculate analytically the topological phase boundary for all interaction and disorder strengths, which has been thought to be only accessible numerically. We discover a regime in which moderate disorder in the interaction matrix elements enhances topological order well into the strongly interacting regime $U > t$. We a…
