arXiv subjects

Moshe Goldstein

Publications and source records attributed to Moshe Goldstein.

At least 37 records · Page 2Linked to original sources

arXiv2025

Transient dynamical phase diagram of the spin-boson model

We investigate the real-time dynamics of the sub-Ohmic spin-boson model across a broad range of coupling strengths, using the numerically exact inchworm quantum Monte Carlo algorithm. From short- and intermediate-time dynamics starting from an initially decoupled state, we extract signatures of the zero-temperature quantum phase transition between localized and delocalized states. We show that the dynamical phase diagram thus obtained differs from the equilibrium phase diagram in both the values of critical couplings and the associated values of the critical exponent. We also identify and quantitatively analyze two competing mechanisms for the crossover between coherent oscillations and incoherent decay. Deep in the sub-Ohmic regime, the crossover is driven by the damping of the oscillation amplitude, while closer to the Ohmic regime the oscillation frequency itself drops sharply to zero at large coupling.

cond-mat.str-el↗

arXiv2024

Relevance of Anisotropy in the Kondo Effect: Lessons From the Symplectic Case

A Kondo model with symplectic symmetry was recently put forward as the effective low-energy theory of a superconducting-island device coupled to multiple leads. This model, which possesses non-Fermi liquid physics and effective anyons, was argued to belong to the class of topological Kondo effects. Here, we clarify the extent of stability of its exotic fixed point using perturbative and numerical renormalization group in conjunction with bosonization and conformal field theory. In contrast to previous claims, we show that asymmetry in the coupling to the leads destabilizes the non-Fermi liquid. Other destabilizing perturbations include asymmetry in the superconducting pairing or internal energy of the individual quantum dots in the island. Nevertheless, these perturbations all generate the same relevant operators. Thus, only a small number of couplings need to be tuned individually, and these can be selected according to experimental convenience. Our results highlight a common misconception that anisotropy in single-channel Kondo couplings is always irrelevant. As demonstrated, relevant terms will emerge whenever the group generators do not span the full space of impurity operators. This calls for a more detailed inspection of models that exhibit this property, such as large-spin impurities and SO(M) Kondo models.

cond-mat.str-el↗

arXiv2024

Quantum metric dependent anomalous velocity in systems subject to complex electric fields

Berry phases have long been known to significantly alter the properties of periodic systems, resulting in anomalous terms in the semiclassical equations of motion describing wave-packet dynamics. In non-Hermitian systems, generalizations of the Berry connection have been proposed and shown to have novel effects on dynamics and transport. In this work, we consider perturbing fields which are themselves non-Hermitian, in the form of complex external electric fields, which are realizable as gain/loss gradients. We derive the full set of semiclassical equations of motion and show that the anomalous velocity depends not only on the Berry curvature, but on the entirety of the quantum geometric tensor, including the quantum metric. This quantum metric dependent velocity appears regardless of whether the unperturbed Hamiltonian is Hermitian or not. These analytical results are compared with numerical lattice simulations which reveal these anomalous terms even in one-dimension. Our work expands the range of phenomena expected to be detectable in experimental setups, which should be realizable in currently available metamaterials and classical wave systems, including mechanical, acoustic, and optical.

cond-mat.mes-hall↗

arXiv2024

Neural Network Ground State from the Neural Tangent Kernel Perspective: The Sign Bias

Neural networks has recently attracted much interest as useful representations of quantum many body ground states, which might help address the infamous sign problem. Most attention was directed at their representability properties, while possible limitations on finding the desired optimal state have not been suitably explored. By leveraging well-established results applicable in the context of infinite width, specifically regarding the renowned neural tangent kernel and conjugate kernel, a comprehensive analysis of the convergence and initialization characteristics of the method is conducted. We reveal the dependence of these characteristics on the interplay among these kernels, the Hamiltonian, and the basis used for its representation. We introduce and motivate novel performance metrics and explore the condition for their optimization. By leveraging these findings, we elucidate a substantial dependence of the effectiveness of this approach on the selected basis, demonstrating that so-called stoquastic Hamiltonians are more amenable to solution through neural networks than those suffering from a sign problem.

quant-ph↗

arXiv2024

Drag conductance induced by neutral-mode localization in fractional quantum Hall junctions

A junction of two 2/3 fractional quantum Hall (FQH) edges, with no charge tunneling between them, may exhibit Anderson localization of neutral modes. Manifestations of such localization in transport properties of the junction are explored. There are two competing localization channels, ``neutral-mode superconductivity'' and ``neutral-mode backscattering''. Localization in any of these channels leads to an effective theory of the junction that is characteristic for FQH effect of bosons, with a minimal integer excitation charge equal to two, and with elementary quasiparticle charge equal to 2/3. These values can be measured by studying shot noise in tunneling experiments. Under the assumption of ballistic transport in the arms connecting the junction to contacts, the two-terminal conductance of the junction is found to be 4/3 for the former localization channel and 1/3 for the latter. The four-terminal conductance matrix reveals in this regime a strong quantized drag between the edges induced by neutral-mode localization. The two localization channels lead to opposite signs of the drag conductance, equal to $\pm 1/4$, which can also be interpreted as a special type of Andreev scattering. Coherent random tunneling in arms of the device (which are segments of 2/3 edges) leads to strong mesoscopic fluctuations of the conductance matrix. In the case of fully equilibrated arms, transport via the junction is insensitive to neutral-mode localization: The two-terminal conductance is quantized to 2/3 and the drag is absent.

cond-mat.mes-hall↗

arXiv2024

Shot noise as a diagnostic in the $ν=2/3$ fractional quantum Hall edge zoo

The $ν= 2/3$ filling is the simplest paradigmatic example of a fractional quantum Hall state, which contains counter-propagating edge modes. These modes can be either in the unequilibrated regime or equilibrated to different extents, on top of a possible edge reconstruction. In the unequilibrated regime, two distinct renormalization group fixed points have been previously proposed, namely Kane-Fischer-Polchinski and Wang-Meir-Gefen. In the equilibration regime, different degree of thermal equilibration may occur, while charge is fully equilibrated. Here, we show that this rich variety of models can give rise to three possible conductance plateaus at $e^2/2h$ (recently observed in experiments), $5e^2/9h$ (predicted here), and $e^2/3h$ (observed earlier in experiments) in a quantum point contact geometry. We identify different mechanisms for \emph{electrical shot noise} generation at these plateaus, which provides an experimentally accessible venue for distinguishing among the distinct models.

cond-mat.mes-hall↗

arXiv2024

Extensive Long-Range Entanglement at Finite Temperatures from a Nonequilibrium Bias

Thermal equilibrium states of local quantum many-body systems are notorious for their spatially decaying correlations, which place severe restrictions on the types of many-body entanglement structures that may be observed at finite temperatures. These restrictions may however be defied when an out-of-equilibrium steady state is considered instead. In this paper, we study the entanglement properties of free fermions on a one-dimensional lattice that contains a generic charge- and energy-conserving noninteracting impurity, and that is connected at its edges to two reservoirs with different equilibrium energy distributions. These distributions may differ in either temperature, chemical potential, or both, thereby inducing an external bias. We analytically derive exact asymptotic expressions for several quantum information measures -- the mutual information, its Rényi generalizations, and the fermionic negativity -- that quantify the correlation and entanglement between two subsystems located on opposite sides of the impurity. We show that all these measures scale (to a leading order) linearly with the overlap between one subsystem and the mirror image of the other (upon reflection of the latter about the impurity), independently of the distance between the subsystems. While a simple proportionality relation between the negativity and Rényi versions of the mutual information is observed to hold at zero temperature, it breaks down at finite temperatures, suggesting that these quantities represent strong long-range correlations of different origins. Our results generalize previous findings that were limited to the case of a chemical-potential bias at zero temperature, rigorously demonstrating that the effect of long-range volume-law entanglement is robust at finite temperatures.

quant-ph↗

arXiv2024

Inelastic decay from integrability

A hallmark of integrable systems is the purely elastic scattering of their excitations. Such systems possess an extensive number of locally conserved charges, leading to the conservation of the number of scattered excitations, as well as their set of individual momenta. In this work, we show that inelastic decay can nevertheless be observed in circuit QED realizations of integrable boundary models. We consider the scattering of microwave photons off impurities in superconducting circuits implementing the boundary sine-Gordon and Kondo models, which are both integrable. We show that not only inelastic decay is possible for the microwave photons, in spite of integrability, and thanks to a nonlinear relation between them and the elastically-scattered excitations, but also that integrability in fact provides powerful analytical tools allowing to obtain exact expressions for response functions describing the inelastic decay. Using the framework of form factors, we calculate the total inelastic decay rate and elastic phase shift of the microwave photons, extracted from a 2-point response function. We then go beyond linear response and obtain the exact energy-resolved inelastic decay spectrum, using a novel method to evaluate form factor expansions of 3-point response functions, which could prove useful in other applications of integrable quantum field theories. We relate our results to several recent photon splitting experiments, and in particular to recent experimental data that provides evidence for the elusive Schmid-Bulgadaev dissipative quantum phase transition.

quant-ph↗

arXiv2024

Exact asymptotics of long-range quantum correlations in a nonequilibrium steady state

Out-of-equilibrium states of many-body systems tend to evade a description by standard statistical mechanics, and their uniqueness is epitomized by the possibility of certain long-range correlations that cannot occur in equilibrium. In quantum many-body systems, coherent correlations of this sort may lead to the emergence of remarkable entanglement structures. In this work, we analytically study the asymptotic scaling of quantum correlation measures -- the mutual information and the fermionic negativity -- within the zero-temperature steady state of voltage-biased free fermions on a one-dimensional lattice containing a noninteracting impurity. Previously, we have shown that two subsystems on opposite sides of the impurity exhibit volume-law entanglement, which is independent of the absolute distances of the subsystems from the impurity. Here we go beyond that result and derive the exact form of the subleading logarithmic corrections to the extensive terms of correlation measures, in excellent agreement with numerical calculations. In particular, the logarithmic term of the mutual information asymptotics can be encapsulated in a concise formula, depending only on simple four-point ratios of subsystem length-scales and on the impurity scattering probabilities at the Fermi energies. This echoes the case of equilibrium states, where such logarithmic terms may convey universal information about the physical system. To compute these exact results, we devise a hybrid method that relies on Toeplitz determinant asymptotics for correlation matrices in both real space and momentum space, successfully circumventing the inhomogeneity of the system. This method can potentially find wider use for analytical calculations of entanglement measures in similar scenarios.

quant-ph↗

arXiv2024

Superselection-Resolved Entanglement in Lattice Gauge Theories: A Tensor Network Approach

Lattice gauge theories (LGT) play a central role in modern physics, providing insights into high-energy physics, condensed matter physics, and quantum computation. Due to the nontrivial structure of the Hilbert space of LGT systems, entanglement in such systems is tricky to define. However, when one limits themselves to superselection-resolved entanglement, that is, entanglement corresponding to specific gauge symmetry sectors (commonly denoted as superselection sectors), this problem disappears, and the entanglement becomes well-defined. The study of superselection-resolved entanglement is interesting in LGT for an additional reason: when the gauge symmetry is strictly obeyed, superselection-resolved entanglement becomes the only distillable contribution to the entanglement. In our work, we study the behavior of superselection-resolved entanglement in LGT systems. We employ a tensor network construction for gauge-invariant systems as defined by Zohar and Burrello (2016) and find that, in a vast range of cases, the leading term in superselection-resolved entanglement depends on the number of corners in the partition, that is, corner-law entanglement. To our knowledge, this is the first case of such a corner-law being observed in any lattice system.

quant-ph↗

arXiv2023

Full Classification of Transport on an Equilibrated 5/2 Edge via Shot Noise

The nature of the bulk topological order of the 5/2 non-Abelian fractional quantum Hall state and the steady-state of its edge are long-studied questions. The most promising non-Abelian model bulk states are the Pfaffian (Pf), anti-Pffafian (APf), and particle-hole symmetric Pfaffian (PHPf). Here, we propose to employ a set of dc current-current correlations \emph{(electrical shot noise)} in order to distinguish among the Pf, APf, and PHPf candidate states, as well as to determine their edge thermal equilibration regimes: full vs.\ partial. Using other tools, measurements of GaAs platforms have already indicated consistency with the PHPf state. Our protocol, realizable with available experimental tools, is based on fully electrical measurements.

cond-mat.mes-hall↗

arXiv2023

Extensive Long-Range Entanglement in a Nonequilibrium Steady State

Entanglement measures constitute powerful tools in the quantitative description of quantum many-body systems out of equilibrium. We study entanglement in the current-carrying steady state of a paradigmatic one-dimensional model of noninteracting fermions at zero temperature in the presence of a scatterer. We show that disjoint intervals located on opposite sides of the scatterer, and within similar distances from it, maintain volume-law entanglement regardless of their separation, as measured by their fermionic negativity and coherent information. The mutual information of the intervals, which quantifies the total correlations between them, follows a similar scaling. Interestingly, this scaling entails in particular that if the position of one of the intervals is kept fixed, then the correlation measures depend non-monotonically on the distance between the intervals. By deriving exact expressions for the extensive terms of these quantities, we prove their simple functional dependence on the scattering probabilities, and demonstrate that the strong long-range entanglement is generated by the coherence between the transmitted and reflected parts of propagating particles within the bias-voltage window. The generality and simplicity of the model suggest that this behavior should characterize a large class of nonequilibrium steady states.

quant-ph↗

arXiv2023

Segmented Composite Design of Robust Single-Qubit Quantum Gates

Error mitigation schemes and error-correcting codes have been the center of much effort in quantum information processing research over the last few decades. While most of the successful proposed schemes for error mitigation are perturbative in the noise and assume deterministic systematic errors, studies of the problem considering the full noise and errors distribution are still scarce. In this work, we introduce an error mitigation scheme for robust single-qubit unitary gates based on composite segmented design, which accounts for the full distribution of the physical noise and errors in the system. We provide two optimization approaches to construct these robust segmented gates: perturbative and non-perturbative, that addresses all orders of errors. We demonstrate our scheme in the photonics realm for the dual-rail directional couplers realization. We show that the 3-segmented composite design for the fundamental single-qubits unitary operations reduces the error by an order of magnitude for a realistic distribution of errors, and that the two approaches are compatible for small errors. This is shown to significantly reduce the overhead of modern error correction codes. Our methods are rather general and can be applied to other realizations of quantum information processing units.

quant-ph↗

arXiv2023

Spontaneous Electric Polarization in Graphene Polytypes

A crystalline solid is a periodic sequence of identical cells, each containing one or more atoms. If the constituting unit cell is not centrosymmetric, charge may distribute unevenly between the atoms, resulting in internal electric polarization. This effect serves as the basis for numerous ferroelectric, piezoelectric, and pyroelectric phenomena. In nearly all polar materials, including multilayered van der Waals stacks that were recently found to exhibit interfacial polarization, inversion symmetry is broken by having two or more atomic species within the unit cell. Here, we show that even elemental crystals, consisting of one type of atom, and composed of non-polar centrosymmetric layers, exhibit electric polarization if arranged in an appropriate three-dimensional architecture. This concept is demonstrated here for inversion and mirror asymmetric mixed-stacking tetra-layer polytypes of non-polar graphene sheets. Furthermore, we find that the room temperature out-of-plane electric polarization increases with external electrostatic doping, rather than decreases owing to screening. Using first-principles calculations, as well as tight-binding modeling, we unveil the origin of polytype-induced polarization and its dependence on doping. Extension of this idea to graphene multilayers suggests that solely by lateral shifts of constituent monolayers one can obtain multiple meta-stable interlayer stacking sequences that may allow for even larger electrical polarization.

cond-mat.mtrl-sci↗

arXiv2023

Chiral numerical renormalization group

The interplay between the Kondo screening of quantum impurities (by the electronic channels to which they couple) and the interimpurity RKKY interactions (mediated by the same channels) has been extensively studied. However, the effect of unidirectional channels (e.g., chiral or helical edge modes of 2D topological materials) which greatly restrict the mediated interimpurity interactions, has only more recently come under scrutiny, and it can drastically alter the physics. Here we take Wilson's numerical renormalization group (NRG), the most established numerical method for treating quantum impurity models, and extend it to systems consisting of two impurities coupled at different locations to unidirectional channel(s). This is challenging due to the incompatibility of unidirectionality with one of the main ingredients in NRG -- the mapping of the channel(s) to a Wilson chain -- a tight-binding chain with the impurity at one end and hopping amplitudes which decay exponentially with the distance. We bridge this gap by introducing a "Wilson ladder" consisting of two coupled Wilson chains, and demonstrate that this construction successfully captures the unidirectionality of the channel(s), as well as the distance between the two impurities. We use this mapping in order to study two Kondo impurities coupled to a single chiral channel, showing that all local properties and thermodynamic quantities are indifferent to the interimpurity distance, and correspond to two separate single-impurity models. Extensions to more impurities and/or helical channels are possible.

cond-mat.str-el↗

arXiv2023

Observation of the Schmid-Bulgadaev dissipative quantum phase transition

Although quantum mechanics applies to many macroscopic superconducting devices, one basic prediction remained controversial for decades. Namely, a Josephson junction connected to a resistor must undergo a dissipation-induced quantum phase transition from superconductor to insulator once the resistor's value exceeds $h/4e^2 \approx 6.5~\textrm{k}Ω$ ($h$ is Planck's constant, $e$ is the electron charge). Here we finally demonstrate this transition by observing the resistor's internal dynamics. Implementing our resistor as a long transmission line section, we find that a junction scatters electromagnetic excitations in the line as either inductance (superconductor) or capacitance (insulator), depending solely on the line's wave impedance. At the phase boundary, the junction itself acts as ideal resistance: in addition to elastic scattering, incident photons can spontaneously down-convert with a frequency-independent probability, which provides a novel marker of quantum-critical behavior.

quant-ph↗

arXiv2023

Manipulating Non-Abelian Anyons in a Chiral Multichannel Kondo Model

Non-Abelian anyons are fractional excitations of gapped topological models believed to describe certain topological superconductors or quantum Hall states. Here, we provide the first numerical evidence that they emerge as independent entities also in gapless electronic models. Starting from a multi-impurity multichannel chiral Kondo model, we introduce a novel mapping to a single-impurity model, amenable to Wilson's numerical renormalization group. We extract its spectral degeneracy structure and fractional entropy, and calculate the $F$ matrices, which encode the topological information regarding braiding of anyons, directly from impurity spin-spin correlations. Impressive recent advances on realizing multichannel Kondo systems with chiral edges may thus bring anyons into reality sooner than expected.

cond-mat.str-el↗

arXiv2023

Generalized topological bulk-edge correspondence in bulk-Hermitian continuous systems with non-Hermitian boundary conditions

The bulk-edge correspondence (BEC) is the hallmark of topological systems. In continuous (nonlattice) Hermitian systems with an unbounded wave vector, it was recently shown that the BEC of Chern insulators is modified. How would it be further affected in non-Hermitian systems, experiencing loss and/or gain? In this work, we take the first step in this direction, by studying a bulk-Hermitian continuous system with non-Hermitian boundary conditions. We find in this case that edge modes emerge at the roots of the scattering matrix, as opposed to the Hermitian case, where they emerge at its poles (or, more accurately, coalescence of roots and poles). This entails a nontrivial modification to the relative Levinson's theorem. We then show that the topological structure remains the same as in the Hermitian case, and the generalized BEC holds, provided one employs appropriately modified contours in the wave-vector plane so that the scattering matrix phase winding counts the edge modes correctly. We exemplify all this using a paradigmatic model of waves in a shallow ocean or active systems in the presence of odd viscosity, as well as 2D electron gas with Hall viscosity. We use this opportunity to examine the case of large odd viscosity, where the scattering matrix becomes $2\times2$, which has not been discussed in previous works on the Hermitian generalized BEC.

cond-mat.mes-hall↗