arXiv subjects

Jan Carl Budich

Publications and source records attributed to Jan Carl Budich.

At least 37 records · Page 2Linked to original sources

arXiv2023

Adiabatic preparation of fractional Chern insulators from an effective thin-torus limit

We explore the quasi one-dimensional (thin torus, or TT) limit of fractional Chern insulators (FCIs) as a starting point for their adiabatic preparation in quantum simulators. Our approach is based on tuning the hopping amplitude in one direction as an experimentally amenable knob to dynamically change the effective aspect ratio of the system. Similar to the TT limit of fractional quantum Hall (FQH) systems in the continuum, we find that the hopping-induced TT limit adiabatically connects the FCI state to a trivial charge density wave (CDW) ground state. This adiabatic path may be harnessed for state preparation schemes relying on the initialization of a CDW state followed by the adiabatic decrease of a hopping anisotropy. Our findings are based on the calculation of the excitation gap in a number of FCI models, both on a lattice and consisting of coupled wires. By analytical calculation of the gap in the limit of strongly anisotropic hopping, we show that its scaling is compatible with the preparation of large size FCIs for sufficiently large hopping anisotropy. Our numerical simulations in the framework of exact diagonalization explore the full anisotropy range to corroborate these results.

cond-mat.quant-gas↗

arXiv2023

Quench-Probe Setup as Analyzer of Fractionalized Entanglement Spreading

We propose a novel spatially inhomogeneous setup for revealing quench-induced fractionalized excitations in entanglement dynamics. In this quench-probe setting, the region undergoing a quantum quench is tunnel-coupled to a static region, the probe.Subsequently, the time-dependent entanglement signatures of a tunable subset of excitations propagating to the probe are monitored by energy selectivity. We exemplify the power of this generic approach by identifying a unique dynamical signature associated with the presence of an isolated Majorana zero mode in the post-quench Hamiltonian. In this case excitations emitted from the topological part of the system give rise to a fractionalized jump of $\log(2)/2$ in the entanglement entropy of the probe. This dynamical effect is highly sensitive to the localized nature of the Majorana zero mode, but does not require the preparation of a topological initial state.

quant-ph↗

arXiv2022

Topological Burning Glass Effect

We reveal a topological burning glass effect, where the local response of a system exhibits a topological quantization that is enhanced by an integer due to its environmental coupling. As a paradigmatic platform for this intriguing phenomenon, we study a central spin that is quasiperiodically driven by two incommensurate frequencies, and statically coupled to $N-1$ surrounding spins. In the strong coupling regime, the adiabatic dynamics of the total system is readily understood to imprint on the central spin an $N$-fold enhanced topological frequency conversion between the two driving frequencies. We argue that the topological burning glass effect is induced by the non-unitary dynamics of the central spin, which locally involves the collective motion of the surrounding spins. Our results are derived in the framework of adiabatic perturbation theory and fully corroborated by exact numerical simulations.

cond-mat.mes-hall↗

arXiv2022

Transition from metal to higher-order topological insulator driven by random flux

Random flux is commonly believed to be incapable of driving full metal-insulator transitions in non-interacting systems. Here we show that random flux can after all induce a full metal-band insulator transition in the two-dimensional Su-Schrieffer-Heeger model. Remarkably, we find that the resulting insulator can be an extrinsic higher-order topological insulator with zero-energy corner modes in proper regimes, rather than a conventional Anderson insulator. Employing both level statistics and finite-size scaling analysis, we characterize the metal-band insulator transition and numerically extract its critical exponent as $ν=2.48\pm0.08$. To reveal the physical mechanism underlying the transition, we present an effective band structure picture based on the random flux averaged Green's function.

cond-mat.mes-hall↗

arXiv2022

Mesoscopic transport signatures of disorder-induced non-Hermitian phases

We investigate the impact on basic quantum transport properties of disorder-induced exceptional points (EPs) that emerge in a disorder-averaged Green's function description of two-dimensional (2D) Dirac semimetals with spin- or orbital-dependent potential scattering. Remarkably, we find that EPs may promote the nearly vanishing conductance of a finite sample at the Dirac point to a sizable value that increases with disorder strength. This striking behavior exhibits a strong directional anisotropy that is closely related to the Fermi arcs connecting the EPs. We corroborate our results by numerically exact simulations, thus revealing the fingerprints of characteristic non-Hermitian spectral features also on the localization properties of the considered systems. Finally, several candidates for the experimental verification of our theoretical analysis are discussed, including disordered electronic square-net materials and cold atoms in spin-dependent optical lattices.

cond-mat.mes-hall↗

arXiv2022

Quantum Non-Hermitian Topological Sensors

We investigate in the framework of quantum noise theory how the striking boundary-sensitivity recently discovered in the context of non-Hermitian (NH) topological phases may be harnessed to devise novel quantum sensors. Specifically, we study a quantum-optical setting of coupled modes arranged in an array with broken ring geometry that would realize a NH topological phase in the classical limit. Using methods from quantum-information theory of Gaussian states, we show that a small coupling induced between the ends of the broken ring may be detected with a precision that increases exponentially in the number of coupled modes, e.g. by heterodyne detection of two output modes. While this robust effect only relies on reaching a NH topological regime, we identify a resonance phenomenon without direct classical counterpart that provides an experimental knob for drastically enhancing the aforementioned exponential growth. Our findings pave the way towards designing quantum NH topological sensors (QUANTOS) that may observe with high precision any physical observable that couples to the boundary conditions of the device.

quant-ph↗

arXiv2021

Dissipative preparation of fractional Chern insulators

We report on the numerically exact simulation of the dissipative dynamics governed by quantum master equations that feature fractional quantum Hall states as unique steady states. In particular, for the paradigmatic Hofstadter model, we show how Laughlin states can be to good approximation prepared in a dissipative fashion from arbitrary initial states by simply pumping strongly interacting bosons into the lowest Chern band of the corresponding single-particle spectrum. While pure (up to topological degeneracy) steady states are only reached in the low-flux limit or for extended hopping range, we observe a certain robustness regarding the overlap of the steady state with fractional quantum Hall states for experimentally well-controlled flux densities. This may be seen as an encouraging step towards addressing the long-standing challenge of preparing strongly correlated topological phases in quantum simulators.

cond-mat.str-el↗

arXiv2021

Exceptional Non-Hermitian Phases in Disordered Quantum Wires

We demonstrate the occurrence of nodal non-Hermitian (NH) phases featuring exceptional degeneracies in chiral-symmetric disordered quantum wires, where NH physics naturally arises from the self-energy in a disorder-averaged Green's function description. Notably, we find that at least two nodal points in the clean Hermitian system are required for exceptional points to be effectively stabilized upon adding disorder. We identify and study experimental signatures of our theoretical findings both in the spectral functions and in mesoscopic quantum transport properties of the considered systems. Our results are quantitatively corroborated and exemplified by numerically exact simulations on a microscopic lattice model. The proposed setting provides a conceptually minimal framework for the realization and study of topological NH phases in quantum many-body systems.

cond-mat.mes-hall↗

arXiv2021

Simulating Exceptional Non-Hermitian Metals with Single-Photon Interferometry

We experimentally simulate in a photonic setting non-Hermitian (NH) metals characterized by the topological properties of their nodal band structures. Implementing nonunitary time evolution in reciprocal space followed by interferometric measurements, we probe the complex eigenenergies of the corresponding NH Bloch Hamiltonians, and study in detail the topology of their exceptional lines (ELs), the NH counterpart of nodal lines in Hermitian systems. We focus on two distinct types of NH metals: two-dimensional systems with symmetry-protected ELs, and three-dimensional systems possessing symmetry-independent topological ELs in the form of knots. While both types feature open Fermi surfaces, we experimentally observe their distinctions by analyzing the impact of symmetry-breaking perturbations on the topology of ELs.

quant-ph↗

arXiv2021

Fourth-Order Exceptional Points in Correlated Quantum Many-Body Systems

Non-Hermtian (NH) Hamiltonians effectively describing the physics of dissipative systems have become an important tool with applications ranging from classical meta-materials to quantum many-body systems. Exceptional points, the NH counterpart of spectral degeneracies, are among the paramount phenomena unique to the NH realm. While realizations of second-order exceptional points have been reported in a variety of microscopic models, higher-order ones have largely remained elusive in the many-body context, as they in general require fine tuning in high-dimensional parameter spaces. Here, we propose a microscopic model of correlated fermions in three spatial dimensions and demonstrate the occurrence of interaction-induced fourth-order exceptional points that are protected by chiral symmetry. We demonstrate their stability against symmetry breaking perturbations and investigate their characteristic analytical and topological properties.

cond-mat.str-el↗

arXiv2021

Dynamically Induced Exceptional Phases in Quenched Interacting Semimetals

We report on the dynamical formation of exceptional degeneracies in basic correlation functions of non-integrable one- and two-dimensional systems quenched to the vicinity of a critical point. Remarkably, fine-tuned semi-metallic points in the phase diagram of the considered systems are thereby promoted to topologically robust non-Hermitian (NH) nodal phases emerging in the coherent long-time evolution of a dynamically equilibrating system. In the framework of non-equilibrium Green's function methods within the conserving second Born approximation, we predict observable signatures of these novel NH nodal phases in simple spectral functions as well as in the time-evolution of momentum distribution functions.

cond-mat.mes-hall↗

arXiv2021

Exceptional Topology of Non-Hermitian Systems

The current understanding of the role of topology in non-Hermitian (NH) systems and its far-reaching physical consequences observable in a range of dissipative settings are reviewed. In particular, how the paramount and genuinely NH concept of exceptional degeneracies, at which both eigenvalues and eigenvectors coalesce, leads to phenomena drastically distinct from the familiar Hermitian realm is discussed. An immediate consequence is the ubiquitous occurrence of nodal NH topological phases with concomitant open Fermi-Seifert surfaces, where conventional band-touching points are replaced by the aforementioned exceptional degeneracies. Furthermore, new notions of gapped phases including topological phases in single-band systems are detailed, and the manner in which a given physical context may affect the symmetry-based topological classification is clarified. A unique property of NH systems with relevance beyond the field of topological phases consists of the anomalous relation between bulk and boundary physics, stemming from the striking sensitivity of NH matrices to boundary conditions. Unifying several complementary insights recently reported in this context, a picture of intriguing phenomena such as the NH bulk-boundary correspondence and the NH skin effect is put together. Finally, applications of NH topology in both classical systems including optical setups with gain and loss, electric circuits,s and mechanical systems and genuine quantum systems such as electronic transport settings at material junctions and dissipative cold-atom setups are reviewed.

cond-mat.mes-hall↗

arXiv2020

Non-Hermitian Topological Sensors

We introduce and study a novel class of sensors whose sensitivity grows exponentially with the size of the device. Remarkably, this drastic enhancement does not rely on any fine-tuning, but is found to be a stable phenomenon immune to local perturbations. Specifically, the physical mechanism behind this striking phenomenon is intimately connected to the anomalous sensitivity to boundary conditions observed in non-Hermitian topological systems. We outline concrete platforms for the practical implementation of these non-Hermitian topological sensors (NTOS) ranging from classical meta-materials to synthetic quantum-materials.

cond-mat.mes-hall↗

arXiv2020

Signatures of topology in quantum quench dynamics and their interrelation

Motivated by recent experimental progress in the study of quantum systems far from equilibrium, we investigate the relation between several dynamical signatures of topology in the coherent time-evolution after a quantum quench. Specifically, we study the conditions for the appearance of entanglement spectrum crossings, dynamical quantum phase transitions, and dynamical Chern numbers. For non-interacting models, we show that in general there is no direct relation between these three quantities. Instead, we relate the presence of level crossings in the entanglement spectrum to localized boundary modes that may not be of topological origin in the conventional sense. Finally, we investigate how interactions influence the presence of entanglement spectrum crossings and dynamical quantum phase transitions, by means of time-dependent density matrix renormalization group simulations.

quant-ph↗

arXiv2020

Interacting topological frequency converter

We show that an interacting two-spin model subjected to two circularly polarized drives enables a feasible realization of a correlated topological phase in synthetic dimensions. The topological observable is given by a quantized frequency conversion between the dynamical drives, which is why we coin it the interacting topological frequency converter (ITFC). The ITFC is characterized by the interplay of interaction and synthetic dimension. This gives rise to striking topological phenomena that have no counterpart in the noninteracting regime. By calculating the topological phase diagrams as a function of interaction strength, we predict an enhancement of frequency conversion as a direct manifestation of the correlated topological response of the ITFC.

cond-mat.mes-hall↗

arXiv2020

Bulk-boundary correspondence in non-Hermitian systems: stability analysis for generalized boundary conditions

The bulk-boundary correspondence (BBC), i.e. the direct relation between bulk topological invariants defined for infinite periodic systems and the occurrence of protected zero-energy surface states in finite samples, is a ubiquitous and widely observed phenomenon in topological matter. In non-Hermitian generalizations of topological systems, however, this fundamental correspondence has recently been found to be qualitatively altered, largely owing to the sensitivity of non-Hermitian eigenspectra to changing the boundary conditions. In this work, we report on two contributions towards comprehensively explaining this remarkable behavior unique to non-Hermitian systems with theory. First, we analytically solve paradigmatic non-Hermitian topological models for their zero-energy modes in the presence of generalized boundary conditions interpolating between open and periodic boundary conditions, thus explicitly following the breakdown of the conventional BBC. Second, addressing the aforementioned spectral fragility of non-Hermitian matrices, we investigate as to what extent the modified non-Hermitian BBC represents a robust and generically observable phenomenon.

cond-mat.mes-hall↗

arXiv2019

Stability of dynamical quantum phase transitions in quenched topological insulators: From multiband to disordered systems

Dynamical quantum phase transitions (DQPTs) represent a counterpart in non-equilibrium quantum time evolution of thermal phase transitions at equilibrium, where real time becomes analogous to a control parameter such as temperature. In quenched quantum systems, recently the occurrence of DQPTs has been demonstrated, both with theory and experiment, to be intimately connected to changes of topological properties. Here, we contribute to broadening the systematic understanding of this relation between topology and DQPTs to multi-orbital and disordered systems. Specifically, we provide a detailed ergodicity analysis to derive criteria for DQPTs in all spatial dimensions, and construct basic counter-examples to the occurrence of DQPTs in multi-band topological insulator models. As a numerical case study illustrating our results, we report on microscopic simulations of the quench dynamics in the Harper-Hofstadter model. Furthermore, going gradually from multi-band to disordered systems, we approach random disorder by increasing the (super) unit cell within which random perturbations are switched on adiabatically. This leads to an intriguing order of limits problem which we address by extensive numerical calculations on quenched one-dimensional topological insulators and superconductors with disorder.

cond-mat.quant-gas↗

arXiv2019

Topological Field Theory far from Equilibrium

The observable properties of topological quantum matter are often described by topological field theories. We here demonstrate that this principle extends beyond thermal equilibrium. To this end, we construct a model of two-dimensional driven open dynamics with a Chern insulator steady state. Within a Keldysh field theory approach, we show that under mild assumptions - particle number conservation and purity of the stationary state - an abelian Chern-Simons theory describes its response to external perturbations. As a corollary, we predict chiral edge modes stabilized by a dissipative bulk.

cond-mat.stat-mech↗