arXiv subjects

Benjamin Béri

Publications and source records attributed to Benjamin Béri.

At least 37 records · Page 2Linked to original sources

arXiv2022

Local integrals of motion detection of localization-protected topological order

Many-body-localized (MBL) phases can be topologically distinct, but distinguishing these phases using order parameters can be challenging. Here we show how topologically distinct local integrals of motion, variationally parametrized by quantum circuits, can be used to numerically demonstrate the topological inequivalence of MBL phases. We illustrate our approach on a fermionic chain where both topologically distinct MBL phases and benchmark comparisons to order parameters are possible. We also use our approach, augmented by the DMRG-X algorithm, to extract high-energy topological doublets. We describe applying our methods to higher dimensions to identify MBL topological order and topological multiplets hidden by the dense many-body spectrum.

cond-mat.dis-nn↗

arXiv2022

Fermion-Parity-Based Computation and its Majorana-Zero-Mode Implementation

Majorana zero modes (MZMs) promise a platform for topologically protected fermionic quantum computation. However, creating multiple MZMs and generating (directly or via measurements) the requisite transformations (e.g., braids) pose significant challenges. We introduce fermion-parity-based computation (FPBC): a measurement-based scheme, modeled on Pauli-based computation, that uses efficient classical processing to virtually increase the number of available MZMs and which, given magic state inputs, operates without transformations. FPBC requires all MZM parities to be measurable, but this conflicts with constraints in proposed MZM hardware. We thus introduce a design in which all parities are directly measurable and which is hence well suited for FPBC. While developing FPBC, we identify the "logical braid group" as the fermionic analog of the Clifford group.

quant-ph↗

arXiv2022

Sachdev-Ye-Kitaev circuits for braiding and charging Majorana zero modes

The Sachdev-Ye-Kitaev (SYK) model is an all-to-all interacting Majorana fermion model for many-body quantum chaos and the holographic correspondence. Here we construct fermionic all-to-all Floquet quantum circuits of random four-body gates designed to capture key features of SYK dynamics. Our circuits can be built using local ingredients in Majorana devices, namely charging-mediated interactions and braiding Majorana zero modes. This offers an analog-digital route to SYK quantum simulations that reconciles all-to-all interactions with the topological protection of Majorana zero modes, a key feature missing in existing proposals for analog SYK simulation. We also describe how dynamical, including out-of-time-ordered, correlation functions can be measured in such analog-digital implementations by employing foreseen capabilities in Majorana devices.

cond-mat.dis-nn↗

arXiv2021

Quantum tunneling in the presence of a topology-changing fermionic bath

Coupling a quantum particle to a fermionic bath suppresses the particle's amplitude to tunnel, even at zero temperature. While this effect can generally be neglected for gapped baths -- a key feature for superconducting qubits -- , it is possible for the bath to be gapped near the potential minima between which the particle tunnels, but different minima to correspond to different bath topologies. This enforces the bath to undergo gap closing along the tunneling path. In this work, we investigate quantum tunneling in the presence of such a topology-changing fermionic bath. We develop a field theory for this problem, linking the instantons describing tunneling in a bath of $d$ space dimensions to topological boundary modes of systems in $d+1$ dimensions, thus stepping a level higher in a dimensional hierarchy. We study in detail a $d=1$ example, inspired by planar Josephson junctions where the particle coordinate is the superconducting phase whose value sets the electronic topology. We find that the topology change suppresses tunneling by a factor scaling exponentially with the system size. This translates to a correspondingly enhanced suppression of the energy splitting for the lowest-lying states, despite these being linear combinations of states near potential minima where the bath is gapped. Our results help to estimate the influence of charging energy on topological phases arising due to the Josephson effect and, conversely, to assess the potential utility of such topological systems as superconducting qubits. For moderate-sized baths, the incomplete suppression of tunneling opens the prospects of quantum-mechanical superpositions of many-body states of different topology, including superpositions of states with and without Majorana fermions.

cond-mat.mes-hall↗

arXiv2020

Strong zero modes from geometric chirality in quasi-one-dimensional Mott insulators

Strong zero modes provide a paradigm for quantum many-body systems to encode local degrees of freedom that remain coherent far from the ground state. Example systems include $\mathbb{Z}_n$ chiral quantum clock models with strong zero modes related to $\mathbb{Z}_n$ parafermions. Here we show how these models and their zero modes arise from geometric chirality in fermionic Mott insulators, focusing on $n=3$ where the Mott insulators are three-leg ladders. We link such ladders to $\mathbb{Z}_3$ chiral clock models by combining bosonization with general symmetry considerations. We also introduce a concrete lattice model which we show to map to the $\mathbb{Z}_3$ chiral clock model, perturbed by the Uimin-Lai-Sutherland Hamiltonian arising via superexchange. We demonstrate the presence of strong zero modes in this perturbed model by showing that correlators of clock operators at the edge remain close to their initial value for times exponentially long in the system size, even at infinite temperature.

cond-mat.str-el↗

arXiv2020

Local Integrals of Motion for Topologically Ordered Many-Body Localized Systems

Many-body localized (MBL) systems are often described using their local integrals of motion, which, for spin systems, are commonly assumed to be a local unitary transform of the set of on-site spin-z operators. We show that this assumption cannot hold for topologically ordered MBL systems. Using a suitable definition to capture such systems in any spatial dimension, we demonstrate a number of features, including that MBL topological order, if present: (i) is the same for all eigenstates; (ii) is robust in character against any perturbation preserving MBL; (iii) implies that on topologically nontrivial manifolds a complete set of integrals of motion must include nonlocal ones in the form of local-unitary-dressed noncontractible Wilson loops. Our approach is well suited for tensor-network methods, and is expected to allow these to resolve highly-excited finite-size-split topological eigenspaces despite their overlap in energy. We illustrate our approach on the disordered Kitaev chain, toric code, and X-cube model.

cond-mat.dis-nn↗

arXiv2020

Supersymmetry in the nonsupersymmetric Sachdev-Ye-Kitaev model

Supersymmetry is a powerful concept in quantum many-body physics. It helps to illuminate ground state properties of complex quantum systems and gives relations between correlation functions. In this work, we show that the Sachdev-Ye-Kitaev model, in its simplest form of Majorana fermions with random four-body interactions, is supersymmetric. In contrast to existing explicitly supersymmetric extensions of the model, the supersymmetry we find requires no relations between couplings. The type of supersymmetry and the structure of the supercharges are entirely set by the number of interacting Majorana modes, and are thus fundamentally linked to the model's Altland-Zirnbauer classification. The supersymmetry we uncover has a natural interpretation in terms of a one-dimensional topological phase supporting Sachdev-Ye-Kitaev boundary physics, and has consequences away from the ground state, including in $q$-body dynamical correlation functions.

cond-mat.str-el↗

arXiv2020

Second-Order Bulk-Boundary Correspondence in Rotationally Symmetric Topological Superconductors from Stacked Dirac Hamiltonians

Two-dimensional second-order topological superconductors host zero-dimensional Majorana bound states at their boundaries. In this work, focusing on rotation-invariant crystalline topological superconductors, we establish a bulk-boundary correspondence linking the presence of such Majorana bound states to bulk topological invariants introduced by Benalcazar et al. We thus establish when a topological crystalline superconductor protected by rotational symmetry displays second-order topological superconductivity. Our approach is based on stacked Dirac Hamiltonians, using which we relate transitions between topological phases to the transformation properties between adjacent gapped boundaries. We find that in addition to the bulk rotational invariants, the presence of Majorana boundary bound states in a given geometry depends on the interplay between weak topological invariants and the location of the rotation center relative to the lattice. We provide numerical examples for our predictions and discuss possible extensions of our approach.

cond-mat.mes-hall↗

arXiv2020

Symmetry classes, many-body zero modes, and supersymmetry in the complex Sachdev-Ye-Kitaev model

The complex Sachdev-Ye-Kitaev (cSYK) model is a charge-conserving model of randomly interacting fermions. The interaction term can be chosen such that the model exhibits chiral symmetry. Then, depending on the charge sector and the number of interacting fermions, level spacing statistics suggests a fourfold categorization of the model into the three Wigner-Dyson symmetry classes. In this work, inspired by previous findings for the Majorana Sachdev-Ye-Kitaev model, we embed the symmetry classes of the cSYK model in the Altland-Zirnbauer framework and identify consequences of chiral symmetry originating from correlations across different charge sectors. In particular, we show that for an odd number of fermions, the model hosts exact many-body zero modes that can be combined into a generalized fermion that does not affect the system's energy. This fermion directly leads to quantum-mechanical supersymmetry that, unlike explicitly supersymmetric cSYK constructions, does not require fine-tuned couplings, but only chiral symmetry. Signatures of the generalized fermion, and thus supersymmetry, include the long-time plateau in time-dependent correlation functions of fermion-parity-odd observables: The plateau may take nonzero value only for certain combinations of the fermion structure of the observable and the system's symmetry class. We illustrate our findings through exact diagonalization simulations of the system's dynamics.

hep-th↗

arXiv2019

Fractional topological insulator precursors in spin-orbit fermion ladders

We study precursor states of fractional topological insulators (FTIs) in interacting fermionic ladders with spin-orbit coupling. Within a microscopically motivated bosonization approach, we investigate different competing phases depending on same-spin and interspin interactions at fractional effective filling $ν=1/3$ per spin. In the spin-decoupled limit, we find that strong repulsive interactions of already moderate range may lead to a partially gapped state with two time-reversed copies of a quasi-one dimensional Laughlin phase. This FTI precursor competes with an interleg partially gapped phase displaying quasi long-range density wave order, however it may be stabilized if interactions have suitable anisotropy, or are sufficiently near SU($2$) symmetry, in leg space. When the FTI phase is present, it is moderately robust to small interspin interactions; these introduce competing partially gapped phases of orbital antiferromagnetic and bond density wave character. Performing a strong coupling analysis of the FTI precursor regime, we find that the main effect of interspin interactions is to induce correlated quasiparticle backscattering between the precursor FTI edge modes. Although this process competes with the topological phase, we show, by considering an array of ladders, that its influence may disappear upon approaching the two dimensional case. Considering time-reversal symmetry breaking perturbations, we also describe a protocol that adiabatically pumps $1/6$ charge per half-cycle, thus providing a quantized FTI signature arising already in the single ladder regime.

cond-mat.str-el↗

arXiv2019

Strictly local tensor networks for short-range topological insulators

Despite the success in describing a range of quantum many-body states using tensor networks, there is a no-go theorem that rules out strictly local tensor networks as topologically nontrivial groundstates of gapped parent Hamiltonians with short-range (including exponentially decaying) couplings. In this work, we show that for free fermions, strictly local tensor networks may describe nonzero temperature averages with respect to gapped Hamiltonians with exponentially decaying couplings. Parent Hamiltonians in this sense may be constructed for any dimensionality and without any obstructions due to their topology. Conversely, we also show that thermal averages with respect to gapped, strictly short-range free-fermion Hamiltonians can be calculated by tensor networks whose links decay exponentially with distance. We also describe a truncation-reconstruction scheme for such tensor networks that leads to a controlled approximation of exact averages in terms of a sequence of related thermal averages. We illustrate our scheme on the two-dimensional Haldane honeycomb model considering both topological and nontopological phases.

cond-mat.mes-hall↗

arXiv2019

The tenfold way and many-body zero modes in the Sachdev-Ye-Kitaev model

The Sachdev-Ye-Kitaev (SYK) model, in its simplest form, describes $k$ Majorana fermions with random all-to-all four-body interactions. We consider the SYK model in the framework of a many-body Altland-Zirnbauer classification that sees the system as belonging to one of eight (real) symmetry classes depending on the value of $k\mod 8$. We show that, depending on the symmetry class, the system may support exact many-body zero modes with the symmetries also dictating whether these may have a nonzero contribution to Majorana fermions, i.e., single-particle weight. These zero modes appear in all but two of the symmetry classes. When present, they leave clear signatures in physical observables that go beyond the threefold (Wigner-Dyson) possibilities for level spacing statistics studied earlier. Signatures we discover include a zero-energy peak or hole in the single-particle spectral function, depending on whether symmetries allow or forbid zero modes to have single-particle weight. The zero modes are also shown to influence the many-body dynamics, where signatures include a nonzero long-time limit for the out-of-time-order correlation function. Furthermore, we show that the extension of the four-body SYK model by quadratic terms can be interpreted as realizing the remaining two complex symmetry classes; we thus demonstrate how the entire tenfold Altland-Zirnbauer classification may emerge in the SYK model.

cond-mat.dis-nn↗

arXiv2017

Observation of photonic Fermi arcs in topological metamaterials

The discovery of topological phases introduces new perspectives and platforms for various interesting physics originally investigated in quantum context and then, on an equal footing, in classic wave systems, such as photonics, acoustics and mechanics. As a characteristic feature, nontrivial Fermi arcs, connecting between topologically distinct Fermi surfaces, play vital roles in the clarification of Dirac and Weyl semimetals and have been observed in quantum materials very recently. However, in classical systems, no direct experimental observation of Fermi arcs in the momentum space has been reported so far. Here, using near-field scanning measurements, we show the observation of a photonic Fermi arcs connecting topologically distinct bulk states in chiral hyperbolic metamaterials. To verify the topological nature of this system, we further observe backscattering-immune propagation of nontrivial surface wave across a three-dimension physical step. Our results demonstrate metamaterial approach towards topological photonics and offer a deeper understanding of topological phases in three-dimension classical systems.

physics.optics↗

arXiv2015

Plasmon Weyl Degeneracies in Magnetized Plasma

In this letter, we report the presence of novel type of plasmon Weyl points in a naturally existing material - magnetized plasma. In such a medium, conventional, purely longitudinal bulk plasma oscillations exists only along the direction of applied magnetic field (z direction). With strong enough magnetic field, there exist helical propagating modes along z direction with circular polarizations. The orthogonality between the longitudinal bulk plasmon mode and the transverse helical propagating modes guarantees their crossing at the bulk plasmon frequency. These crossing points, embedded in the bulk plasmon dispersion line, serve as monopoles in the k space - the so called Weyl points. These Weyl points lead to salient observable features. These include the highly intriguing observation that, at a magnetized plasma surface which is parallel to the applied magnetic field, reflection of an electromagnetic wave with in-plane wave-vector close to the Weyl points exhibits chiral behavior only in half of the k plane, which is bounded by the projection of the bulk plasmon dispersion line. We also verify the presence of 'Fermi arcs' connecting the two Weyl points with opposite chiralities when magnetized plasma interfaces with trivial photonic materials. Our study introduces the concept of Weyl photonics into homogeneous strongly dispersive photonic materials, which could pave way for realizing new topological photonic devices.

physics.optics↗

arXiv2015

Universality and quantized response in bosonic nonfractionalized tunneling

We show that tunneling involving bosonic wires and/or boson integer quantum Hall (bIQH) edges is characterized by universal features which are absent in their fermionic counterparts. Considering a pair of minimal geometries, we find a low energy enhancement and a universal high versus zero energy relation for the tunnel conductance that holds for all wire/bIQH edge combinations. Features distinguishing bIQH edges include a current imbalance to chemical potential bias ratio that is quantized despite the lack of conductance quantization in the bIQH edges themselves. The predicted phenomena require only initial states to be thermal and thus are well suited for tests with ultracold bosons forming wires and bIQH states. For the latter, we highlight a potential realization based on single component bosons in the recently observed Harper-Hofstadter bandstructure.

cond-mat.mes-hall↗

arXiv2014

Topological Photonic Phase in Chiral Hyperbolic Metamaterials

Recently the possibility of achieving one-way backscatter immune transportation of light by mimicking the topological order present within certain solid state systems, such as topological insulators, has received much attention. Thus far however, demonstrations of non-trivial topology in photonics have relied on photonic crystals with precisely engineered lattice structures, periodic on the scale of the operational wavelength and composed of finely tuned, complex materials. Here we propose a novel effective medium approach towards achieving topologically protected photonic surface states robust against disorder on all length scales and for a wide range of material parameters. Remarkably, the non-trivial topology of our metamaterial design results from the Berry curvature arising from the transversality of electromagnetic waves in a homogeneous medium. Our investigation therefore acts to bridge the gap between the advancing field of topological band theory and classical optical phenomena such as the Spin Hall effect of light. The effective medium route to topological phases will pave the way for highly compact one-way transportation of electromagnetic waves in integrated photonic circuits.

physics.optics↗

arXiv2013

Conductance fingerprint of Majorana fermions in the topological Kondo effect

We consider an interacting nanowire/superconductor heterostructure attached to metallic leads. The device is described by an unusual low-energy model involving spin-1 conduction electrons coupled to a nonlocal spin-1/2 Kondo impurity built from Majorana fermions. The topological origin of the resulting Kondo effect is manifest in distinctive non-Fermi-liquid (NFL) behavior, and the existence of Majorana fermions in the device is demonstrated unambiguously by distinctive conductance lineshapes. We study the physics of the model in detail, using the numerical renormalization group, perturbative scaling and abelian bosonization. In particular, we calculate the full scaling curves for the differential conductance in AC and DC fields, onto which experimental data should collapse. Scattering t-matrices and thermodynamic quantities are also calculated, recovering asymptotes from conformal field theory. We show that the NFL physics is robust to asymmetric Majorana-lead couplings, and here we uncover a duality between strong and weak coupling. The NFL behavior is understood physically in terms of competing Kondo effects. The resulting frustration is relieved by inter-Majorana coupling which generates a second crossover to a regular Fermi liquid.

cond-mat.str-el↗

arXiv2013

Gauge Dynamics and Topological Insulators

A non-abelian magnetic field in Yang-Mills theory induces the formation of a "W-boson" vortex lattice. We study the propagation of fundamental fermions in the presence of this lattice in 2+1 dimensions. We show that the spectrum for massless fermions contains four topologically-protected Dirac points with non-zero Bloch momentum. For massive fermions, we compute topological invariants of the band structure and show that it is possible to realise a Z2 topological insulator within Yang-Mills theory.

hep-th↗