arXiv subjects

Shinsei Ryu

Publications and source records attributed to Shinsei Ryu.

At least 91 records · Page 5Linked to original sources

arXiv2020

Gauging anomalous unitary operators

Boundary theories of static bulk topological phases of matter are obstructed in the sense that they cannot be realized on their own as isolated systems. The obstruction can be quantified/characterized by quantum anomalies, in particular when there is a global symmetry. Similarly, topological Floquet evolutions can realize obstructed unitary operators at their boundaries. In this paper, we discuss the characterization of such obstructions by using quantum anomalies. As a particular example, we discuss time-reversal symmetric boundary unitary operators in one and two spatial dimensions, where the anomaly emerges as we gauge the so-called Kubo-Martin-Schwinger (KMS) symmetry. We also discuss mixed anomalies between particle number conserving U(1) symmetry and discrete symmetries, such as C and CP, for unitary operators in odd spatial dimensions that can be realized at the boundaries of topological Floquet systems in even spatial dimensions.

cond-mat.str-el↗

arXiv2020

Anyonic Partial Transpose I: Quantum Information Aspects

A basic diagnostic of entanglement in mixed quantum states is known as the partial transpose and the corresponding entanglement measure is called the logarithmic negativity. Despite the great success of logarithmic negativity in characterizing bosonic many-body systems, generalizing the partial transpose to fermionic systems remained a technical challenge until recently when a new definition that accounts for the Fermi statistics was put forward. In this paper, we propose a way to generalize the partial transpose to anyons with (non-Abelian) fractional statistics based on the apparent similarity between the partial transpose and the braiding operation. We then define the anyonic version of the logarithmic negativity and show that it satisfies the standard requirements such as monotonicity to be an entanglement measure. In particular, we elucidate the properties of the anyonic logarithmic negativity by computing it for a toy density matrix of a pair of anyons within various categories. We conjecture that the subspace of states with a vanishing logarithmic negativity is a set of measure zero in the entire space of anyonic states, in contrast with the ordinary qubit systems where this subspace occupies a finite volume. We prove this conjecture for multiplicity-free categories.

quant-ph↗

arXiv2020

The quasi-particle picture and its breakdown after local quenches: mutual information, negativity, and reflected entropy

We study the dynamics of (Rényi) mutual information, logarithmic negativity, and (Rényi) reflected entropy after exciting the ground state by a local operator. Together with recent results from Ref. [1], we are able to conjecture a close-knit structure between the three quantities that emerges in states excited above the vacuum, including both local and global quantum quenches. This structure intimately depends on the chaoticity of the theory i.e. there exist distinct sets of equivalences for integrable and chaotic theories. For rational conformal field theories (RCFT), we find all quantities to compute the quantum dimension of the primary operator inserted. In contrast, we find the correlation measures to grow (logarithmically) without bound in all $c > 1$ conformal field theories with a finite twist gap. In comparing the calculations in the two classes of theories, we are able to identify the dynamical mechanism for the breakdown of the quasi-particle picture in 2D conformal field theories. Intriguingly, we also find preliminary evidence that our general lessons apply to quantum systems considerably distinct from conformal field theories, such as integrable and chaotic spin chains, suggesting a universality of entanglement dynamics in non-equilibrium systems.

hep-th↗

arXiv2020

Conformal field theory and the web of quantum chaos diagnostics

We study three prominent diagnostics of chaos and scrambling in the context of two-dimensional conformal field theory: the spectral form factor, out-of-time-ordered correlators, and unitary operator entanglement. With the observation that all three quantities may be obtained by different analytic continuations of the torus partition function, we address the connections and distinctions between the information that each quantity provides us. In this process, we study the emergence of irrationality from "large-N" limits of rational conformal field theories (RCFTs) as well as the explicit breakdown of rationality for theories with central charges greater than the number of their conserved currents. Our analysis begins to elucidate the intermediate dynamical behavior of theories that bridge the gap between integrable RCFTs and maximally chaotic holographic CFTs.

hep-th↗

arXiv2020

Transport across twist angle domains in moiré graphene

Many of the experiments in twisted bilayer graphene (TBG) differ from each other in terms of the details of their phase diagrams. Few controllable aspects aside, this discrepancy is largely believed to be arising from the presence of a varying degree of twist angle inhomogeneity across different samples. Real space maps indeed reveal TBG devices splitting into several large domains of different twist angles. Motivated by these observations, we study the quantum mechanical tunneling across a domain wall (DW) that separates two such regions. We show that the tunneling of the moiré particles can be understood by the formation of an effective step potential at the DW. The height of this step potential is simply a measure of the difference in twist angles. These computations lead us to identify the global transport signatures for detecting and quantifying the local twist angle variations. In particular, Using Landauer-Büttiker formalism we compute single-channel conductance ($dI/dV$) and Fano factor for shot noise (ratio of noise power and mean current). A zero-bias, sub-meV transport gap is observed in the conductance which scales with the height of the step potential. One of the key findings of our work is that transport in presence of twist angle inhomogeneity is "noisy", though sub-Poissonian. In particular, the differential Fano factor peaks near the van Hove energies corresponding to the domains in the sample. The location and the strength of the peak is simply a measure of the degree of twist angle inhomogeneity.

cond-mat.mes-hall↗

arXiv2020

Entanglement spectrum and entropy in topological non-Hermitian systems and non-unitary conformal field theories

We propose a method of computing and studying entanglement quantities in non-Hermitian systems by use of a biorthogonal basis. We find that the entanglement spectrum characterizes the topological properties in terms of the existence of mid-gap states in the non-Hermitian Su-Schrieffer-Heeger (SSH) model with parity and time-reversal symmetry (PT symmetry) and the non-Hermitian Chern insulators. In addition, we find that at a critical point in the PT symmetric SSH model, the entanglement entropy has a logarithmic scaling with corresponding central charge $c=-2$. This critical point then is a free-fermion lattice realization of the non-unitary conformal field theory.

cond-mat.str-el↗

arXiv2020

The negativity contour: a quasi-local measure of entanglement for mixed states

In this paper, we study the entanglement structure of mixed states in quantum many-body systems using the $\textit{negativity contour}$, a local measure of entanglement that determines which real-space degrees of freedom in a subregion are contributing to the logarithmic negativity and with what magnitude. We construct an explicit contour function for Gaussian states using the fermionic partial-transpose. We generalize this contour function to generic many-body systems using a natural combination of derivatives of the logarithmic negativity. Though the latter negativity contour function is not strictly positive for all quantum systems, it is simple to compute and produces reasonable and interesting results. In particular, it rigorously satisfies the positivity condition for all holographic states and those obeying the quasi-particle picture. We apply this formalism to quantum field theories with a Fermi surface, contrasting the entanglement structure of Fermi liquids and holographic (hyperscale violating) non-Fermi liquids. The analysis of non-Fermi liquids show anomalous temperature dependence of the negativity depending on the dynamical critical exponent. We further compute the negativity contour following a quantum quench and discuss how this may clarify certain aspects of thermalization.

hep-th↗

arXiv2020

Correlation measures and the entanglement wedge cross-section after quantum quenches in two-dimensional conformal field theories

We consider the time evolution of mixed state correlation measures in two-dimensional conformal field theories, such as logarithmic negativity, odd entropy, and reflected entropy, after quantum quenches of various kinds. These correlation measures, in the holographic context, are all associated to the entanglement wedge cross section. We contrast various classes of conformal field theories, both rational and irrational (pure) conformal field theories. First, for rational conformal field theories, whose dynamics can be well described by the quasi-particle picture, we find all four quantities for disjoint intervals to be proportional, regardless of the specific quench protocol. Second, using the light cone bootstrap, we generalize our results to irrational conformal field theories where we find sharp distinctions from the quasi-particle results and striking differences between mutual information and the other measures. The large surplus of logarithmic negativity relative to mutual information forces us to reconsider what mutual information and logarithmic negativity really measure. We interpret these results as a signature of information scrambling and chaos in irrational theories. These CFT results perfectly agree with our gravitational (holographic) calculations. Furthermore, using holography, we are able to generalize the results to outside of the light cone limit. Finally, due to the breakdown of the quasi-particle picture for irrational theories, we appeal to the "line-tension picture," motivated by random unitary circuits, as a phenomenological description. We observe that random unitary circuits, with local Hilbert space dimension determined by the Cardy formula, have precisely the same entanglement dynamics as irrational (including holographic) conformal field theories.

hep-th↗

arXiv2019

Quantum vs. classical information: operator negativity as a probe of scrambling

We consider the logarithmic negativity and related quantities of time evolution operators. We study free fermion, compact boson, and holographic conformal field theories (CFTs) as well as numerical simulations of random unitary circuits and integrable and chaotic spin chains. The holographic behavior strongly deviates from known non-holographic CFT results and displays clear signatures of maximal scrambling. Intriguingly, the random unitary circuits display nearly identical behavior to the holographic channels. Generically, we find the "line-tension picture" to effectively capture the entanglement dynamics for ergodic systems and the "quasi-particle picture" for integrable systems. With this motivation, we propose an effective line-tension that captures the dynamics of the logarithmic negativity in ergodic systems in the spacetime scaling limit. We compare the negativity and mutual information leading us to find distinct dynamics of quantum and classical information. The "spurious entanglement" we observe may have implications on the "simulatability" of quantum systems on classical computers. Finally, we elucidate the connection between the operation of partially transposing a density matrix in conformal field theory and the entanglement wedge cross section in Anti-de Sitter space using geodesic Witten diagrams.

hep-th↗

arXiv2019

Non-local order parameters for states with topological electromagnetic response

Chern insulators are states of matter characterized by a quantized Hall conductance, gapless edge modes but also a singular response to monopole configurations of an external electromagnetic field. In this paper, we describe the nature of such a singular response and show how it can be used to define a class of operators acting as non-local order parameters. These operators characterize the Chern-insulator states in the following way: for a given state, there exists a corresponding operator which has an algebraically decaying two-point function in that particular state, while it decays exponentially in all other states. The behaviour of the order parameter is defined only in terms of the electromagnetic response, and not from any microscopic properties, and we therefore claim to have found a generic order parameter for the Chern insulating states. We support this claim by numerically evaluating the order parameters for different insulating states. We also show how our construction can be generalized to other states with topological electromagnetic response, and use the states with a quantized magnetoelectric effect in three dimensions as an example. Besides providing novel insights into topological states of matter, our construction can be exploited to efficiently diagnose such states numerically.

cond-mat.str-el↗

arXiv2019

Particle Number Fluctuations, Rényi and Symmetry-resolved Entanglement Entropy in Two-dimensional Fermi Gas from Multi-dimensional Bosonization

In this paper, we revisit the computation of particle number fluctuations and the Rényi entanglement entropy of a two-dimensional Fermi gas using multi-dimensional bosonization. In particular, we compute these quantities for a circular Fermi surface and a circular entangling surface. Both quantities display a logarithmic violation of the area law, and the Rényi entropy agrees with the Widom conjecture. Lastly, we compute the symmetry-resolved entanglement entropy for the two-dimensional circular Fermi surface and find that, while the total entanglement entropy scales as $R\log R$, the symmetry-resolved entanglement scales as $\sqrt{R\log R}$, where $R$ is the radius of the subregion of our interest.

cond-mat.stat-mech↗

arXiv2019

Non-local Order Parameters and Quantum Entanglement for Fermionic Topological Field Theories

We study quantized non-local order parameters, constructed by using partial time-reversal and partial reflection, for fermionic topological phases of matter in one spatial dimension protected by an orientation reversing symmetry, using topological quantum field theories (TQFTs). By formulating the order parameters in the Hilbert space of state sum TQFT, we establish the connection between the quantized non-local order parameters and the underlying field theory, clarifying the nature of the order parameters as topological invariants. We also formulate several entanglement measures including the entanglement negativity on state sum spin TQFT, and describe the exact correspondence of the entanglement measures to path integrals on a closed surface equipped with a specific spin structure.

cond-mat.str-el↗

arXiv2019

Collective excitations at filling factor 5/2: The view from superspace

We present a microscopic theory of the neutral collective modes supported by the non-Abelian fractional quantum Hall states at filling factor 5/2. The theory is formulated in terms of the trial states describing the Girvin-MacDonald-Platzman (GMP) mode and its fermionic counterpart. These modes are superpartners of each other in a concrete sense, which we elucidate.

cond-mat.str-el↗

arXiv2019

Effective response theory for Floquet topological systems

We present an effective field theory approach to the topological response of Floquet systems with symmetry group $G$. This is achieved by introducing a background $G$ gauge field in the Schwinger-Keldysh formalism, which is suitable for far from equilibrium systems. We carry out this program for chiral topological Floquet systems (anomalous Floquet-Anderson insulators) in two spatial dimensions, and the group cohomology models of topological Floquet unitaries. These response actions serve as many-body topological invariants for topological Floquet unitaries. The effective action approach also leads us to propose novel topological response functions.

cond-mat.str-el↗

arXiv2019

Holographic entanglement contour, bit threads, and the entanglement tsunami

We study the entanglement contour, a quasi-local measure of entanglement, and propose a generic formula for the contour in 1+1d quantum systems. We use this formalism to investigate the real space entanglement structure of various static CFTs as well as local and global quantum quenches. The global quench elucidates the spatial distribution of entanglement entropy in strongly interacting CFTs and clarifies the interpretation of the entanglement tsunami picture. The entanglement tsunami effectively characterizes the non-local growth of entanglement entropy while the contour characterizes the local propagation of entanglement. We generalize the formula for the entanglement contour to arbitrary dimensions and entangling surface geometries using bit threads, and are able to realize a holographic contour for logarithmic negativity and the entanglement of purification by restricting the bulk spacetime to the entanglement wedge. Furthermore, we explore the connections between the entanglement contour, bit threads, and entanglement density in kinematic space.

hep-th↗

arXiv2019

Twisted and untwisted negativity spectrum of free fermions

A basic diagnostic of entanglement in mixed quantum states is known as the positive partial transpose (PT) criterion. Such criterion is based on the observation that the spectrum of the partially transposed density matrix of an entangled state contains negative eigenvalues, in turn, used to define an entanglement measure called the logarithmic negativity. Despite the great success of logarithmic negativity in characterizing bosonic many-body systems, generalizing the operation of PT to fermionic systems remained a technical challenge until recently when a more natural definition of PT for fermions that accounts for the Fermi statistics has been put forward. In this paper, we study the many-body spectrum of the reduced density matrix of two adjacent intervals for one-dimensional free fermions after applying the fermionic PT. We show that in general there is a freedom in the definition of such operation which leads to two different definitions of PT: the resulting density matrix is Hermitian in one case, while it becomes pseudo-Hermitian in the other case. Using the path-integral formalism, we analytically compute the leading order term of the moments in both cases and derive the distribution of the corresponding eigenvalues over the complex plane. We further verify our analytical findings by checking them against numerical lattice calculations.

cond-mat.stat-mech↗

arXiv2019

Finite-temperature entanglement negativity of free fermions

The entanglement entropy of free fermions with a Fermi surface is known to obey a logarithmic scaling and violate the area law in all dimensions. Here, we would like to see how temperature affects the logarithmic scaling behavior. To this end, we compute the entanglement negativity of free fermions using the fermionic partial transpose developed in our earlier paper [Phys. Rev. B 95, 165101 (2017)]. In one dimension, we analytically derive the leading order term in the finite-temperature entanglement negativity and show how the entanglement negativity indicates a crossover from a quantum entangled state to a classical thermal state, where the entanglement is completely lost. We explain how the one-dimensional result can be generalized to codimension-one Fermi surface of arbitrary shape in higher dimensions. In both one and two dimensions, we check that our analytical results agree with the numerical simulation of free fermions on a lattice.

cond-mat.stat-mech↗

arXiv2019

Entanglement negativity of fermions: monotonicity, separability criterion, and classification of few-mode states

We study quantum information aspects of the fermionic entanglement negativity recently introduced in [Phys. Rev. B 95, 165101 (2017)] based on the fermionic partial transpose. In particular, we show that it is an entanglement monotone under the action of local quantum operations and classical communications--which preserves the local fermion-number parity-- and satisfies other common properties expected for an entanglement measure of mixed states. We present fermionic analogs of tripartite entangled states such as W and Greenberger-Horne-Zeilinger states and compare the results of bosonic and fermionic partial transpose in various fermionic states, where we explain why the bosonic partial transpose fails in distinguishing separable states of fermions. Finally, we explore a set of entanglement quantities which distinguish different classes of entangled states of a system with two and three fermionic modes. In doing so, we prove that vanishing entanglement negativity is a necessary and sufficient condition for separability of $N\geq 2$ fermionic modes with respect to the bipartition into one mode and the rest. We further conjecture that the entanglement negativity of inseparable states which mix local fermion-number parity is always non-vanishing.

quant-ph↗