arXiv subjects

Igor V. Gornyi

Publications and source records attributed to Igor V. Gornyi.

36 records · Page 2Linked to original sources

arXiv2022

Many-body localization in a tilted potential in two dimensions

Thermalization in many-body systems can be inhibited by the application of a linearly increasing potential, which is known as Stark many-body localization. Here we investigate the fate of this phenomenon on a two-dimensional disorder-free lattice with up to $24 \times 6$ sites. Similar to the one-dimensional case, "density-polarized" regions can act as bottlenecks for transport and thermalization on laboratory timescales. However, compared to the one-dimensional case, a substantially stronger potential gradient is needed to prevent thermalization when an extra spatial dimension is involved. The origin of this difference and implications for experiments are discussed. We argue that delocalization is generally favored for typical states in two-dimensional Stark many-body systems, although nonergodicity can still be observed for a specific choice of initial states, such as those probed in experiments.

cond-mat.str-el↗

arXiv2022

Generalized quantum measurements with matrix product states: Entanglement phase transition and clusterization

We propose a method, based on matrix product states, for studying the time evolution of many-body quantum lattice systems under continuous and site-resolved measurement. Both the frequency and the strength of generalized measurements can be varied within our scheme, thus allowing us to explore the corresponding two-dimensional phase diagram. The method is applied to one-dimensional chains of nearest-neighbor interacting hard-core bosons. A transition from an entangling to a disentangling (area-law) phase is found. However, by resolving time-dependent density correlations in the monitored system, we find important differences between different regions at the phase boundary. In particular, we observe a peculiar phenomenon of measurement-induced particle clusterization that takes place only for frequent moderately strong measurements, but not for strong infrequent measurements.

quant-ph↗

arXiv2022

Spin and valley degrees of freedom in a bilayer graphene quantum point contact: Zeeman splitting and interaction effects

We present a study on the lifting of degeneracy of the size-quantized energy levels in an electrostatically defined quantum point contact in bilayer graphene by the application of in-plane magnetic fields. We observe a Zeeman spin splitting of the first three subbands, characterized by effective Landé $g$-factors that are enhanced by confinement and interactions. In the gate-voltage dependence of the conductance, a shoulder-like feature below the lowest subband appears, which we identify as a $0.7$ anomaly stemming from the interaction-induced lifting of the band degeneracy. We employ a phenomenological model of the $0.7$ anomaly to the gate-defined channel in bilayer graphene subject to in-plane magnetic field. Based on the qualitative theoretical predictions for the conductance evolution with increasing magnetic field, we conclude that the assumption of an effective spontaneous spin splitting is capable of describing our observations, while the valley degree of freedom remains degenerate.

cond-mat.mes-hall↗

arXiv2022

Does delta-$T$ noise probe quantum statistics?

We study delta-T noise -- excess charge noise at zero voltage but finite temperature bias -- for weak tunneling in 1D interacting systems. We show that the sign of the delta-T noise is generically determined by the nature of the dominating tunneling process (more specifically, its scaling dimension). We clarify the relation between the sign of delta-T noise and the quantum exchange statistics of tunneling quasiparticles. We find that, for infinite systems hosting chiral channels with local interactions (e.g., quantum Hall or quantum spin Hall edges), when the delta-T noise is negative, the tunneling particles are boson-like, revealing their tendency towards bunching. However, the opposite is not true: Boson-like particles do not necessarily produce negative delta-T noise. Importantly, the bosonic nature of particles generating the negative delta-T is not necessarily intrinsic, but can be induced by the interactions. This particularly implies that negative delta-T noise for tunneling between the edge states cannot serve as a smoking gun for detecting "intrinsic anyons". We also establish a connection between the delta-T noise and the temperature derivative of the thermal noise in interacting systems, both governed by the same scaling dimensions. As a demonstration of the above statements, we study tunneling between two interacting quantum spin Hall edges. With bosonization and renormalization-group techniques, we find that many-body interactions can generate negative delta-T noise for both direct tunneling through a point contact and in Kondo exchange tunneling via a localized spin. In both setups, we show that the noise can become negative at sufficiently low temperatures, when interactions renormalize the tunneling to favor boson-like pair-tunneling of electrons. Our findings show that delta-T noise can probe the nature of collective excitations in interacting 1D systems.

cond-mat.mes-hall↗

arXiv2021

Many-body localization in the interpolating Aubry-André-Fibonacci model

We investigate the localization properties of a spin chain with an antiferromagnetic nearest-neighbour coupling, subject to an external quasiperiodic on-site magnetic field. The quasiperiodic modulation interpolates between two paradigmatic models, namely the Aubry-André and the Fibonacci models. We find that stronger many-body interactions extend the ergodic phase in the former, whereas they shrink it in the latter. Furthermore, the many-body localization transition points at the two limits of the interpolation appear to be continuously connected along the deformation. As a result, the position of the many-body localization transition depends on the interaction strength for an intermediate degree of deformation of the quasiperiodic modulation. Moreover, in the region of parameter space where the single-particle spectrum contains both localized and extended states, many-body interactions induce an anomalous effect: weak interactions localize the system, whereas stronger interactions enhance ergodicity. We map the model's localization phase diagram using the decay of the quenched spin imbalance in relatively long chains. This is accomplished employing a time-dependent variational approach applied to a matrix product state decomposition of the many-body state. Our model serves as a rich playground for testing many-body localization under tunable potentials.

cond-mat.dis-nn↗

arXiv2021

Stark many-body localization: Evidence for Hilbert-space shattering

We study the dynamics of an interacting quantum spin chain under the application of a linearly increasing field. This model exhibits a type of localization known as Stark many-body localization. The dynamics shows a strong dependence on the initial conditions, indicating that the system violates the conventional ("strong") eigenstate thermalization hypothesis at any finite gradient of the field. This is contrary to reports of a numerically observed ergodic phase. Therefore, the localization is crucially distinct from disorder-driven many-body localization, in agreement with recent predictions on the basis of localization via Hilbert-space shattering.

cond-mat.dis-nn↗

arXiv2021

Many-body localization in large systems: Matrix-product-state approach

Recent developments in matrix-product-state (MPS) investigations of many-body localization (MBL) are reviewed, with a discussion of benefits and limitations of the method. This approach allows one to explore the physics around the MBL transition in systems much larger than those accessible to exact diagonalization. System sizes and length scales that can be controllably accessed by the MPS approach are comparable to those studied in state-of-the-art experiments. Results for 1D, quasi-1D, and 2D random systems, as well as 1D quasi-periodic systems are presented. On time scales explored (up to $t \approx 300$ in units set by the hopping amplitude), a slow, subdiffusive transport in a rather broad disorder range on the ergodic side of the MBL transition is found. For 1D random spin chains, which serve as a "standard model" of the MBL transition, the MPS study demonstrates a substantial drift of the critical point $W_c(L)$ with the system size $L$: while for $L \approx 20$ we find $W_c \approx 4$, as also given by exact diagonalization, the MPS results for $L = 50$--100 provide evidence that the critical disorder saturates, in the large-$L$ limit, at $W_c \approx 5.5$. For quasi-periodic systems, these finite-size effects are much weaker, which suggests that they can be largely attributed to rare events. For quasi-1D ($d\times L$, with $d \ll L$) and 2D ($L\times L$) random systems, the MPS data demonstrate an unbounded growth of $W_c$ in the limit of large $d$ and $L$, in agreement with analytical predictions based on the rare-event avalanche theory.

cond-mat.dis-nn↗

arXiv2020

Majorana modes in emergent-wire phases of helical and cycloidal magnet-superconductor hybrids

Noncollinear magnetism opens exciting possibilities to generate topological superconductivity. Here, we focus on helical and cycloidal magnetic textures in magnet-superconductor hybrid structures in a background magnetic field. We demonstrate that this system can enter a topological phase which can be understood as a set of parallel topological wires. We explore and confirm this idea in depth with three different approaches: a continuum model, a tight-binding model based on the magnetic unit cell, and exact diagonalization on a finite two-dimensional lattice. The key signature of this topological state is the presence of Majorana bound states at certain disclination defects in the magnetic texture. Based on the $C_2$ symmetry imposed by the helical or cycloidal texture, we employ the theory of topological crystalline superconductors with rotation invariants to obtain the Majorana parity at disclinations. Furthermore, we consider a 90-degree helimagnet domain wall, which is formed by a string of alternating disclinations. We discuss how the resulting chain of disclination bound states hybridizes into two chiral modes with different velocities. We suggest that hybrid systems of chiral magnets and superconductors are capable of hosting Majorana modes in various spatial configurations with potentially far less nano-engineering than in, e.g., semiconductor wires.

cond-mat.supr-con↗

arXiv2020

Slow many-body delocalization beyond one dimension

We study the delocalization dynamics of interacting disordered hard-core bosons for quasi-1D and 2D geometries, with system sizes and time scales comparable to state-of-the-art experiments. The results are strikingly similar to the 1D case, with slow, subdiffusive dynamics featuring power-law decay. From the freezing of this decay we infer the critical disorder $W_c(L, d)$ as a function of length $L$ and width $d$. In the quasi-1D case $W_c$ has a finite large-$L$ limit at fixed $d$, which increases strongly with $d$. In the 2D case $W_c(L,L)$ grows with $L$. The results are consistent with the avalanche picture of the many-body localization transition.

cond-mat.dis-nn↗

arXiv2020

Dissipation without resistance: Imaging impurities at quantum Hall edges

Motivated by the recent experiment by Marguerite et al. [1] on imaging in graphene samples, we investigate theoretically the dissipation induced by resonant impurities in the quantum Hall regime. The impurity induced forward scattering of electrons at quantum Hall edges leads to an enhanced phonon emission, which reaches its maximum when the impurity state is tuned to resonance by a scanning tip voltage. Our analysis of the effect of the tip potential on the dissipation reveals peculiar thermal rings around the impurities, in consistency with experimental observations. Remarkably, this impurity-induced dissipation reveals non-trivial features that are unique for chiral 1D systems such as quantum Hall edges. First, the dissipation is not accompanied by the generation of resistance. Second, this type of dissipation is highly nonlocal: a single impurity induces heat transfer to phonons along the whole edge.

cond-mat.mes-hall↗

arXiv2019

Majorana bound states in magnetic skyrmions imposed onto a superconductor

We consider a superconducting film exchange-coupled to a close-by chiral magnetic layer and study how magnetic skyrmions can induce the formation of Majorana bound states (MBS) in the superconductor. Inspired by a proposal by Yang et al. [Phys. Rev. B 93, 224505 (2016)], which suggested MBS in skyrmions of even winding number, we explore whether such skyrmions could result from a merger of ordinary skyrmions. We conclude that the formation of higher-winding skyrmions is not realistic in chiral magnets. Subsequently, we present a possibility to obtain MBS from realistic skyrmions of winding number one, if a skyrmion-vortex pair is formed instead of a bare skyrmion. Specifically, we show that MBS are supported in a pair of a circular skyrmion and a vortex which both have a winding number of one. We back up our analytical prediction with results from numerical diagonalization and obtain the spatial profile of the MBS. In light of recent experimental progress on the manipulation of skyrmions, such systems are promising candidates to achieve direct spatial control of MBS.

cond-mat.supr-con↗

arXiv2018

Many-body localization and delocalization in large quantum chains

We theoretically study the quench dynamics for an isolated Heisenberg spin chain with a random on-site magnetic field, which is one of the paradigmatic models of a many-body localization transition. We use the time-dependent variational principle as applied to matrix product states, which allows us to controllably study chains of a length up to $L=100$ spins, i.e., much larger than $L \simeq 20$ that can be treated via exact diagonalization. For the analysis of the data, three complementary approaches are used: (i) determination of the exponent $β$ which characterizes the power-law decay of the antiferromagnetic imbalance with time; (ii) similar determination of the exponent $β_Λ$ which characterizes the decay of a Schmidt gap in the entanglement spectrum, (iii) machine learning with the use, as an input, of the time dependence of the spin densities in the whole chain. We find that the consideration of the larger system sizes substantially increases the estimate for the critical disorder $W_c$ that separates the ergodic and many-body localized regimes, compared to the values of $W_c$ in the literature. On the ergodic side of the transition, there is a broad interval of the strength of disorder with slow subdiffusive transport. In this regime, the exponents $β$ and $β_Λ$ increase, with increasing $L$, for relatively small $L$ but saturate for $L \simeq 50$, indicating that these slow power laws survive in the thermodynamic limit. From a technical perspective, we develop an adaptation of the "learning by confusion" machine learning approach that can determine $W_c$.

cond-mat.dis-nn↗

arXiv2014

Hanbury Brown and Twiss Correlations in Quantum Hall Systems

We study a Hanbury Brown and Twiss (HBT) interferometer formed with chiral edge channels of a quantum Hall system. HBT cross-correlations are calculated for a device operating both in the integer and fractional quantum Hall regimes, the latter at Laughlin filling fractions. We find that in both cases, when the current is dominated by electron tunneling, current-current correlations show antibunching, characteristic of fermionic correlations. When the current-current correlations are dominated by quasiparticle tunneling, the correlations reveal bunching, characteristic of bosons. For electron tunneling we use Keldysh technique, and show that the result for fractional filling factors can be obtained in a simple way from the results of the integer case. It is shown that quasiparticle-dominated cross-current correlations can be analyzed by means of a quantum master equation approach. We present here a detailed derivation of the results of Ref. [Phys. Rev. Lett. 109, 106802 (2012)] and generalize them to all Laughlin fractions.

cond-mat.mes-hall↗

arXiv2012

Hanbury-Brown and Twiss interference of anyons

We present a study of an Hanbury Brown and Twiss (HBT) interferometer realized with anyons. Such a device can directly probe entanglement and fractional statistics of initially uncorrelated particles. We calculate HBT cross-correlations of Abelian Laughlin anyons. The correlations we calculate exhibit partial bunching similar to bosons, indicating a substantial statistical transmuta- tion from the underlying electronic degrees of freedom. We also find qualitative differences between the anyonic signal and the corresponding bosonic or fermionic signals, indicating that anyons cannot be simply thought as intermediate between bosons and fermions.

cond-mat.mes-hall↗

arXiv2012

Weak localization and magnetoresistance in a two-leg ladder model

We analyze the weak localization correction to the conductivity of a spinless two-leg ladder model in the limit of strong dephasing τ_ϕ<< τ_tr, paying particular attention to the presence of a magnetic field, which leads to an unconventional magnetoresistance behavior. We find that the magnetic field leads to three different effects: (i) negative magnetoresistance due to the regular weak localization correction (ii) effective decoupling of the two chains, leading to positive magnetoresistance and (iii) oscillations in the magnetoresistance originating from the nature of the low-energy collective excitations. All three effects can be observed depending on the parameter range, but it turns out that large magnetic fields always decouple the chains and thus lead to the curious effect of magnetic field enhanced localization.

cond-mat.str-el↗

arXiv2012

Manifestation of electron-electron interaction in the magnetoresistance of graphene

We investigate the magnetotransport in large area graphene Hall bars epitaxially grown on silicon carbide. In the intermediate field regime between weak localization and Landau quantization the observed temperature-dependent parabolic magnetoresistivity (MR) is a manifestation of the electron-electron interaction (EEI). We can consistently describe the data with a model for diffusive (magneto)transport that also includes magnetic-field dependent effects originating from ballistic time scales. We find an excellent agreement between the experimentally observed temperature dependence of MR and the theory of EEI in the diffusive regime. We can further assign a temperature-driven crossover to the reduction of the multiplet modes contributing to EEI from 7 to 3 due to intervalley scattering. In addition, we find a temperature independent ballistic contribution to the MR in classically strong magnetic fields.

cond-mat.mes-hall↗

arXiv2002

Quantum critical fluctuations in disordered d-wave superconductors

Quasiparticles in the cuprates appear to be subject to anomalously strong inelastic damping mechanisms. To explain the phenomenon, Sachdev and collaborators recently proposed to couple the system to a critically fluctuating order parameter mode of either id_{xy}- or is-symmetry. Motivated by the observation that the energies relevant for the dynamics of this mode are comparable to the scattering rate induced by even moderate impurity concentrations, we here generalize the approach to the presence of static disorder. In the id-case, we find that the coupling to disorder renders the order parameter dynamics diffusive but otherwise leaves much of the phenomenology observed in the clean case intact. In contrast, the interplay of impurity scattering and order parameter fluctuations of is-symmetry entails the formation of a secondary superconductor transition, with a critical temperature exponentially sensitive to the disorder concentration.

cond-mat.supr-con↗

arXiv1998

Quantum conductivity corrections in two dimensional long-range disordered systems with strong spin-orbit splitting of electron spectrum

We study quantum corrections to conductivity in a 2D system with a smooth random potential and strong spin-orbit splitting of the spectrum. We show that the interference correction is positive and down to the very low temperature can exceed the negative correction related to electron-electron interactions. We discuss this result in the context of the problem of the metal-insulator transition in Si-MOSFET structures.

cond-mat.mes-hall↗