Search for: All records

In two-dimensional topological insulators, a disorder-induced topological phase transition is typically identified with an Anderson localization transition at the Fermi energy. However, in ${\mathbb{Z}}_2$trivial, spin-resolved topological insulators it is the spectral gap of the spin spectrum, in addition to the bulk mobility gap, which protects the nontrivial topology of the ground state. In this work, we show that these two gaps, the bulk electronic and spin gap, can evolve distinctly on the introduction of quenched short-ranged disorder and that an odd-quantized spin Chern number topologically protects states below the Fermi energy from localization. This decoupling leads to a unique situation in which an Anderson localization transition occurs below the Fermi energy at the topological transition. Furthermore, the presence of topologically protected extended bulk states nontrivial bulk topology typically implies the existence of protected boundary modes. We demonstrate the absence of protected boundary modes in the Hamiltonian and yet the edge modes in the eigenstates of the projected spin operator survive. Our work thus provides evidence that a nonzero spin-Chern number, in the absence of a nontrivial ${\mathbb{Z}}_2$index, does not demand the existence of protected boundary modes at finite or zero energy. Published by the American Physical Society2024 

Abstract We investigate the boundary phenomena that arise in a finite-sizeXXspin chain interacting through anXXinteraction with a spin $-\frac{1}{2}$impurity located at its edge. Upon Jordan–Wigner transformation, the model is described by a quadratic Fermionic Hamiltonian. Our work displays, within this ostensibly simple model, the emergence of the Kondo effect, a quintessential hallmark of strongly correlated physics. We also show how the Kondo cloud shrinks and turns into a single particle bound state as the impurity coupling increases beyond a critical value. In more detail, using bothBethe Ansatzandexact diagonalizationtechniques, we show that the local moment of the impurity is screened by different mechanisms depending on the ratio of the boundary and bulk coupling $\frac{J_{\mathrm{imp}}}{J}$. When the ratio falls below the critical value $\sqrt{2}$, the impurity is screened via the Kondo effect. However, when the ratio between the coupling exceeds the critical value $\sqrt{2}$an exponentially localized bound mode is formed at the impurity site which screens the spin of the impurity in the ground state. We show that the boundary phase transition is reflected in local ground state properties by calculating the spinon density of states, the magnetization at the impurity site in the presence of a global magnetic field, and the finite temperature susceptibility of the impurity. We find that the spinon density of states in the Kondo phase has the characteristic Lorentzian peak that moves from the Fermi level to the maximum energy of the spinon as the impurity coupling is increased and becomes a localized bound mode in the bound mode phase. Moreover, the impurity magnetization and the finite temperature impurity susceptibility behave differently in the two phases. When the boundary coupling $J_{\mathrm{imp}}$exceeds the critical value $\sqrt{2}J$, the model is no longer boundary conformal invariant as a massive bound mode appears at the impurity site. 

We study one-dimensional hybrid quantum circuits perturbed by quenched quasiperiodic (QP) modulations across the measurement-induced phase transition (MIPT). Considering non-Pisot QP structures, characterized by unbounded fluctuations, allows us to tune the wandering exponent β to exceed the Luck bound ν ≥ 1/(1−β) for the stability of the MIPT, where ν = 1.28(2). Via robust numerical simulations of random Clifford circuits interleaved with local projective measurements, we find that sufficiently large QP structural fluctuations destabilize the MIPT and induce a flow to a broad family of critical dynamical phase transitions of the infinite QP type that is governed by the wandering exponent β. We numerically determine the associated critical properties, including the correlation length exponent consistent with saturating the Luck bound, and a universal activated dynamical scaling with activation exponent ψ ≅ β, finding excellent agreement with the conclusions of real-space renormalization group calculations. 

Abstract We study non-local measures of spectral correlations and their utility in characterizing and distinguishing between the distinct eigenstate phases of quantum chaotic and many-body localized systems. We focus on two related quantities, the spectral form factor and the density of all spectral gaps, and show that they furnish unique signatures that can be used to sharply identify the two phases. We demonstrate this by numerically studying three one-dimensional quantum spin chain models with (i) quenched disorder, (ii) periodic drive (Floquet), and (iii) quasiperiodic detuning. We also clarify in what ways the signatures are universal and in what ways they are not. More generally, this thorough analysis is expected to play a useful role in classifying phases of disorder systems.