arXiv subjects

Alexander Altland

Publications and source records attributed to Alexander Altland.

At least 55 records · Page 3Linked to original sources

arXiv2019

Non-ergodic extended states in the SYK model

We analytically study spectral correlations and many body wave functions of an SYK-model deformed by a one body contribution to the Hamiltonian. Our main result is the identification of a wide range of intermediate coupling strengths where the spectral statistics is of Wigner-Dyson type, while wave functions are non-uniformly distributed over Fock space and show fractal behavior. The structure of the theory suggests that such manifestations of non-ergodic extendedness may be a prevalent phenomenon in strongly interacting chaotic quantum systems.

cond-mat.str-el↗

arXiv2019

Quantum criticality of granular SYK matter

We consider granular quantum matter defined by Sachdev-Ye-Kitaev (SYK) dots coupled via random one-body hopping. Within the framework of Schwarzian field theory, we identify a zero temperature quantum phase transition between an insulating phase at weak and a metallic phase at strong hopping. The critical hopping strength scales inversely with the number of degrees of freedom on the dots. The increase of temperature out of either phase induces a crossover into a regime of strange metallic behavior.

cond-mat.str-el↗

arXiv2018

Non-Topological Majorana Zero Modes in Inhomogeneous Spin Ladders

We show that the coupling of homogeneous Heisenberg spin-1/2 ladders in different phases leads to the formation of interfacial zero energy Majorana bound states. Unlike Majorana bound states at the interfaces of topological quantum wires, these states are void of topological protection and generally susceptible to local perturbations of the host spin system. However, a key message of our work is that in practice they show a high degree of resilience over wide parameter ranges which may make them interesting candidates for applications.

cond-mat.str-el↗

arXiv2018

Nodal points of Weyl semimetals survive the presence of moderate disorder

In this work we address the physics of individual three dimensional Weyl nodes subject to a moderate concentration of disorder. Previous analysis indicates the presence of a quantum phase transition below which disorder becomes irrelevant and the integrity of sharp nodal points of vanishing spectral density is preserved in this system. This statement appears to be at variance with the inevitable presence of statistically rare fluctuations which cannot be considered as weak and must have strong influence on the system's spectrum, no matter how small the average concentration. We here reconcile the two pictures by demonstrating that rare fluctuation potentials in the Weyl system generate a peculiar type of resonances which carry spectral density in any neighborhood of zero energy, but never at zero. In this way, the vanishing of the DoS for weak disorder survives the inclusion of rare events. We demonstrate this feature by considering three different models of disorder, each emphasizing specific aspects of the problem: a simplistic box potential model, a model with Gaussian distributed disorder, and one with a finite number of $s$-wave scatterers. Our analysis also explains why the protection of the nodal DoS may be difficult to see in simulations of finite size lattices.

cond-mat.dis-nn↗

arXiv2018

Vanishing density of states in weakly disordered Weyl semimetals

The Brillouin zone of the clean Weyl semimetal contains points at which the density of states (DoS) vanishes. Previous work suggested that below a certain critical concentration of impurities this features is preserved including in the presence of disorder. This result got criticized for its neglect of rare disorder fluctuations which might bind quantum states and hence generate a finite DoS. We here show that in spite of their existence these states are so fragile that their contribution effectively vanishes when averaged over continuous disorder distributions. This means that the integrity of the nodal points remains protected for weak disorder.

cond-mat.dis-nn↗

arXiv2017

Quantum ergodicity in the SYK model

We present a replica path integral approach describing the quantum chaotic dynamics of the SYK model at large time scales. The theory leads to the identification of non-ergodic collective modes which relax and eventually give way to an ergodic long time regime (describable by random matrix theory). These modes, which play a role conceptually similar to the diffusion modes of dirty metals, carry quantum numbers which we identify as the generators of the Clifford algebra: each of the $2^N$ different products that can be formed from $N$ Majorana operators defines one effective mode. The competition between a decay rate quickly growing in the order of the product and a density of modes exponentially growing in the same parameter explains the characteristics of the system's approach to the ergodic long time regime. We probe this dynamics through various spectral correlation functions and obtain favorable agreement with existing numerical data.

cond-mat.str-el↗

arXiv2017

Probing the topology of density matrices

The mixedness of a quantum state is usually seen as an adversary to topological quantization of observables. For example, exact quantization of the charge transported in a so-called Thouless adiabatic pump is lifted at any finite temperature in symmetry-protected topological insulators. Here, we show that certain directly observable many-body correlators preserve the integrity of topological invariants for mixed Gaussian quantum states in one dimension. Our approach relies on the expectation value of the many-body momentum-translation operator, and leads to a physical observable --- the "ensemble geometric phase" (EGP) --- which represents a bona fide geometric phase for mixed quantum states, in the thermodynamic limit. In cyclic protocols, the EGP provides a topologically quantized observable which detects encircled spectral singularities ("purity-gap" closing points) of density matrices. While we identify the many-body nature of the EGP as a key ingredient, we propose a conceptually simple, interferometric setup to directly measure the latter in experiments with mesoscopic ensembles of ultracold atoms.

cond-mat.quant-gas↗

arXiv2017

Power-law out of time order correlation functions in the SYK model

We evaluate the finite temperature partition sum and correlation functions of the Sachdev-Ye-Kitaev (SYK) model. Starting from a recently proposed mapping of the SYK model onto Liouville quantum mechanics, we obtain our results by exact integration over conformal Goldstone modes reparameterizing physical time. Perhaps, the least expected result of our analysis is that at time scales proportional to the number of particles the out of time order correlation function crosses over from a regime of exponential decay to a universal $t^{-6}$ power-law behavior.

cond-mat.str-el↗

arXiv2017

Majorana qubits in topological insulator nanoribbon architecture

We describe designs for the realization of topological Majorana qubits in terms of proximitized topological insulator nanoribbons pierced by a uniform axial magnetic field. This platform holds promise for particularly robust Majorana bound states, with easily manipulable inter-state couplings. We propose proof-of-principle experiments for initializing, manipulating, and reading out Majorana box qubits defined in floating devices dominated by charging effects. We argue that the platform offers design advantages which make it particularly suitable for extension to qubit network structures realizing a Majorana surface code.

cond-mat.mes-hall↗

arXiv2016

Effective field theory approach to many-body localization

We construct an analytic theory of many-body localization (MBL) in random spin chains. The approach is based on a first quantized perspective in which MBL is understood as a localization phenomenon on the high dimensional lattice defined by the discrete Hilbert space of the clean system. We construct a field theory on that lattice and apply it to discuss the stability of a weak disorder (`Wigner-Dyson') and a strong disorder (`Poisson') phase.

cond-mat.dis-nn↗

arXiv2016

Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics

We show that the proper inclusion of soft reparameterization modes in the Sachdev-Ye-Kitaev model of $N$ randomly interacting Majorana fermions reduces its long-time behavior to that of Liouville quantum mechanics. As a result, all zero temperature correlation functions decay with the universal exponent $\propto τ^{-3/2}$ for times larger than the inverse single particle level spacing $τ\gg N\ln N$. In the particular case of the single particle Green function this behavior is manifestation of the zero-bias anomaly, or scaling in energy as $ε^{1/2}$. We also present exact diagonalization study supporting our conclusions.

cond-mat.str-el↗

arXiv2016

Sinai Diffusion at Quasi-1D Topological Phase Transitions

We consider critical quantum transport in disordered topological quantum wires at the transition between phases with different topological indexes. Focusing on the example of thermal transport in class D (`Majorana') quantum wires, we identify a transport universality class distinguished for anomalous retardation in the propagation of excitations -- a quantum generalization of Sinai diffusion. We discuss the expected manifestations of this transport mechanism for heat propagation in topological superconductors near criticality and provide a microscopic theory explaining the phenomenon.

cond-mat.mes-hall↗

arXiv2015

Theory of the strongly disordered Weyl semimetal

In disordered Weyl semimetals, mechanisms of topological origin lead to novel mechanisms of transport, which manifest themselves in unconventional types of electromagnetic response. Prominent examples of transport phenomena particular to the Weyl context include the anomalous Hall effect, the chiral magnetic effect, and the formation of totally field dominated regimes of transport in which the longitudinal conductance is proportional to an external magnetic field. In this paper, we discuss the manifestations of these phenomena at large length scales including the cases of strong disorder and/or magnetic field which are beyond the scope of diagrammatic perturbation theory. Our perhaps most striking finding is the identification of a novel regime of drift/diffusion transport where diffusion at short scales gives way to effectively ballistic dynamics at large scales, before a re-entrance to diffusion takes place at yet larger scales. We will show that this regime plays a key role in understanding the interplay of the various types of magnetoresponse of the system. Our results are obtained by describing the strongly disordered system in terms of an effective field theory of Chern-Simons type. The paper contains a self-contained derivation of this theory, and a discussion of both equilibrium and non-equilibrium (noise) transport phenomena following from it.

cond-mat.mes-hall↗

arXiv2015

U(1) and SU(2) quantum dissipative systems: The Caldeira-Leggett vs. the Amegaokar-Eckern-Schön approaches

There are two paradigmatic frameworks for treating quantum systems coupled to a dissipative environment: the Caldeira-Leggett and the Ambegaokar-Eckern-Schön approaches. Here we recall the differences between them, and explain the consequences when each is applied to a zero dimensional spin (possessing an SU(2) symmetry) in a dissipative environment (a dissipative quantum dot near or beyond the Stoner instability point).

cond-mat.mes-hall↗

arXiv2015

Geometric Quantum Noise of Spin

The presence of geometric phases is known to affect the dynamics of the systems involved. Here we consider a quantum degree of freedom, moving in a dissipative environment, whose dynamics is described by a Langevin equation with quantum noise. We show that geometric phases enter the stochastic noise terms. Specifically, we consider small ferromagnetic particles (nano-magnets) or quantum dots close to Stoner instability, and investigate the dynamics of the total magnetization in the presence of tunneling coupling to the metallic leads. We generalize the Ambegaokar-Eckern-Schön (AES) effective action and the corresponding semiclassical equations of motion from the U(1) case of the charge degree of freedom to the SU(2) case of the magnetization. The Langevin forces (torques) in these equations are strongly influenced by the geometric phase. As a first but nontrivial application we predict low temperature quantum diffusion of the magnetization on the Bloch sphere, which is governed by the geometric phase. We propose a protocol for experimental observation of this phenomenon.

cond-mat.mes-hall↗

arXiv2015

Intermediate fixed point in a Luttinger liquid with elastic and dissipative backscattering

In a recent work [Phys. Rev. Lett. {\bf 108}, 136401 (2012)] we have addressed the problem of a Luttinger liquid with a scatterer that allows for both coherent and incoherent scattering channels. We have found that the physics associated with this model is qualitatively different from the elastic impurity setup analyzed by Kane and Fisher, and from the inelastic scattering scenario studied by Furusaki and Matveev, thus proposing a new paradigmatic picture of Luttinger liquid with an impurity. Here we present an extensive study of the renormalization group flows for this problem, the fixed point landscape, and scaling near those fixed points. Our analysis is non-perturbative in the elastic tunneling amplitudes, employing an instanton calculation in one or two of the available elastic tunneling channels. Our analysis accounts for non-trivial Klein factors, which represent anyonic or fermionic statistics. These Klein factors need to be taken into account due to the fact that higher order tunneling processes take place. In particular we find a stable fixed point, where an incoming current is split ${1 \over 2}$ - $1\over 2$ between a forward and a backward scattered beams. This intermediate fixed point, between complete backscattering and full forward scattering, is stable for the Luttinger parameter $g<1$.

cond-mat.mes-hall↗

arXiv2015

Topology vs. Anderson localization: non-perturbative solutions in one dimension

We present an analytic theory of quantum criticality in quasi one-dimensional topological Anderson insulators. We describe these systems in terms of two parameters $(g,χ)$ representing localization and topological properties, respectively. Certain critical values of $χ$ (half-integer for $\Bbb{Z}$ classes, or zero for $\Bbb{Z}_2$ classes) define phase boundaries between distinct topological sectors. Upon increasing system size, the two parameters exhibit flow similar to the celebrated two parameter flow of the integer quantum Hall insulator. However, unlike the quantum Hall system, an exact analytical description of the entire phase diagram can be given in terms of the transfer-matrix solution of corresponding supersymmetric non-linear sigma-models. In $\Bbb{Z}_2$ classes we uncover a hidden supersymmetry, present at the quantum critical point.

cond-mat.mes-hall↗

arXiv2015

Effective field theory of the disordered Weyl semimetal

In disordered Weyl semimetals, mechanisms of topological origin lead to the protection against Anderson localization, and at the same time to different types of transverse electromagnetic response -- the anomalous Hall, and chiral magnetic effect. We here apply field theory methods to discuss the manifestation of these phenomena at length scales which are beyond the scope of diagrammatic perturbation theory. Specifically we show how an interplay of symmetry breaking and the chiral anomaly leads to a field theory containing two types of topological terms. Generating the unconventional response coefficients of the system, these terms remain largely unaffected by disorder, i.e. information on the chirality of the system remains visible even at large length scales.

cond-mat.mes-hall↗