arXiv subjects

Huajia Wang

Publications and source records attributed to Huajia Wang.

At least 19 recordsLinked to original sources

arXiv2026

Lee-Yang paradigm of phase transition in eigenstate thermalized systems

As phase transitions in isolated quantum systems remain elusive, here we show how a thermodynamic-like phase transition, falling into the Lee-Yang paradigm, can arise in systems displaying eigenstate thermalization. Specifically, we show that in holographic conformal field theories, the eigenstate expectation of the auto-correlation function can be mapped to the partition function ${\cal Z}_{gauge}(z)$ of a virtual interacting instanton gas, with the conformal mapping of the imaginary time: $z=1-e^{-τ}$ and the central charge $c$ mimicking the instanton fugacity and volume, respectively. We find that akin to the Lee-Yang paradigm, for $c\to\infty$ a pair of complex conjugate zeros of ${\cal Z}_{gauge}(z)$ move to the real axis located at the famous forbidden singularity. Passing through the singularity the system transits from the low- to high-fugacity phase, accompanied by dramatic changes in scaling behaviors of the free energy and dominant microscopic configurations. Our findings indicate that physics of phase transitions from eigenstate thermalization is very rich.

hep-th↗

arXiv2026

Phase transition from eigenstate thermalization: forbidden singularity and instanton proliferation via AGT correspondence

In theoretical physics, finding connections between problems that appear in distinct contexts is an important way to leapfrog progresses, often by illuminating deep aspects that may otherwise seem obscure. In this paper, we consider in 2d CFTs the phenomenon of forbidden singularities in auto-correlation functions -- a key signature of eigenstate thermalization. We show that they correspond to phase transitions in the context of eigenstates. The connection is made explicit by utilizing the AGT correspondence, which relates eigenstate auto-correlations to the Nekrasov partition functions describing an instanton gas of the $\mathcal{N}=2$ SUSY gauge theories. We show that by taking the counter-part of the heavy-light limit, two phases emerge for the instanton gas. They are dominated by configurations represented by string-like Young tableaux with distinct structures and thermodynamic properties, which bare resemblance to the confined and the deconfined phases. A phase transition occurs as instantons proliferate from one side, in a manner that mimics the Lee-Yang theory. We work out the critical fugacity and find it corresponding exactly to the forbidden singularity.

hep-th↗

arXiv2025

Non-perturbative aspects of entanglement structures in $T\bar{T}$-deformed CFTs

Turning on the $T\bar{T}$-deformation in a two-dimensional CFT provides a unique window to study explicitly how non-local features arise in the UV as a result of the deformation. A sharp signature is the dynamical emergence of an effective length-scale $\propto \sqrtμ$ that separates the local and non-local regimes of the deformed theory, effectively serving as a UV cut-off for computing observables in the local regime. In this paper, we study this phenomenon through the entanglement structures of the deformed theory. We focus on computing the Renyi entropies of single-interval sub-regions in the deformed vacuum states. We pay particular attention to the interplay between the bare entanglement cut-off inherited from the CFT computation and the effects from the $T\bar{T}$ deformations. Applying the general replica trick to the string theory formulation of $T\bar{T}$-deformed CFTs, we derive an explicit representation of the deformed replica partition function as a weighted integral of the CFT results evaluated at a dynamical cut-off, which is integrated over. We computed in detail the kernel functions of the integral representation, and performed the saddle-point analysis in the semi-classical limit of small $μ$. We found that in addition to the perturbative saddle-point which identifies the dynamical cut-off with the bare entanglement cut-off, there exists another non-perturbative saddle-point that identifies the dynamical cut-off with the $T\bar{T}$ length-scale $\propto \sqrtμ$, but whose contribution is exponentially small. We discuss how these non-perturbative effects can shed lights on the mechanism through which the $T\bar{T}$ length-scale may eventually replace the bare counter-part and become the effective entanglement cut-off.

hep-th↗

arXiv2025

Non-local modular flows across deformed null-cuts

Modular flows probe important aspects of the entanglement structures, especially those of QFTs, in a dynamical framework. Despite the expected non-local nature in the general cases, the majority of explicitly understood examples feature local space-time trajectories under modular flows. In this work, we study a particular class of non-local modular flows. They are associated with the relativistic vacuum state and sub-regions whose boundaries lie on a planar null-surface. They satisfy a remarkable algebraic property known as the half-sided modular inclusion, and as a result the modular Hamiltonians are exactly known in terms of the stress tensor operators. To be explicit, we focus on the simplest QFT of a massive or massless free scalar in $2+1$ dimensions. We obtain explicit expressions for the generators. They can be separated into a sum of local and non-local terms showing certain universal pattern. The preservation of von-Neumann algebra under modular flow works in a subtle way for the non-local terms. We derive a differential-integral equation for the finite modular flow, which can be analyzed in perturbation theory of small distance deviating from the entanglement boundary, and re-summation can be performed in appropriate limits. Comparison with the general expectation of modular flows in such limits are discussed.

hep-th↗

arXiv2025

Resurgent properties of $T\overline{T}$-deformed conformal field theories

We elaborate on the resurgence analysis on the $T\overline{T}$-deformed 2d conformal field theory (CFT). Writing the deformed partition function as an infinite series in the deformation parameter $λ$, we develop efficient analytical methods to compute high-order terms of the $λ$-series. Based on the asymptotic behavior of the large-order perturbative series, we show that the $λ$-series is asymptotic and extract non-perturabtive contributions by resurgence. This paper extends a previous Letter of the same authors to interacting rational CFTs, with Lee-Yang CFT as a concrete example. We also discuss possible implications of the resurgence results on holography.

hep-th↗

arXiv2024

Holographic Renyi entropy of 2d CFT in KdV generalized ensemble

The eigenstate thermalization hypothesis (ETH) in chaotic two dimensional CFTs is subtle due to infinitely many conserved KdV charges. Previous works have demonstrated that primary CFT eigenstates have flat entanglement spectrum, which is very different from the microcanonical ensemble. This result is an apparent contradiction to conventional ETH, which does not take KdV charges into account. In a companion paper \cite{KdVETHgeneral}, we resolve this discrepancy by studying the subsystem entropy of a chaotic CFT in KdV-generalized Gibbs and microcanonical ensembles. In this paper, we carry out parallel computations in the context of AdS/CFT. We focus on the high density limit, which is equivalent to thermodynamic limit in conformal theories. In this limit holographic Renyi entropy can be computed using the so-called gluing construction. We explicitly study the KdV-generalized microcanonical ensemble with the densities of the first two KdV charges $\langle \mathcal{Q}_1\rangle = q_1,\langle \mathcal{Q}_3\rangle = q_3$ fixed and obeying $q_3-q_1^2 \ll q_1^2$. In this regime we found that the refined Renyi entropy $\tilde{S}_n$ is $n$-independent for $n>n_{cut}$, where $n_{cut}$ depends on $q_1,q_3$. By taking the primary state limit $q_3\to q_1^2$, we recover flat entanglement spectrum characteristic of fixed-area states, in agreement with the primary state behavior. This provides a consistency check of the KdV-generalized ETH in 2d CFTs.

hep-th↗

arXiv2024

Resurgence of $T\bar{T}$-deformed Partition Function

We study non-perturbative effects of torus partition function of the $T\bar{T}$-deformed 2d CFTs by resurgence. The deformed partition function can be written as an infinite series of the deformation parameter $λ$. We develop highly efficient methods to compute perturbative coefficients in the $λ$ expansion. To exemplify, the first 600 coefficients for the $T\bar{T}$-deformed free boson and free fermion are computed. Equipped with the large order perturbative data, we provide convincing numerical evidence that the $λ$ expansion series is asymptotic and not Borel resummable. We extract the non-perturbative contribution by resurgence and propose that they originate from new complex saddle points after analytically continuing the modular parameters in the integral representation of the partition function. The proposal is checked by comparing the predicted asymptotic behavior of the coefficients and large order perturbative data, which match nicely. The implications of these non-perturbative contributions for the Stokes phenomenon, which relates the positive and negative signs of $λ$, is also discussed.

hep-th↗

arXiv2024

Subsystem entropy in 2d CFT and KdV ETH

We study subsystem entropy in 2d CFTs, for subsystems constituting a finite fraction of the full system. We focus on the extensive contribution, which scales linearly with the subsystem size in the thermodynamic limit. We employ the so-called diagonal approximation to evaluate subsystem entropy for the chaotic CFTs in thermal state (canonical ensemble), microcanonical ensemble, and in a primary state, matching previously known results. We then proceed to find analytic expressions for the subsystem entropy at leading order in $c$, when the global CFT state is the KdV generalized Gibbs ensemble or the KdV microcanonical ensemble. Previous studies of primary eigenstates have shown that, akin to fixed-area states in AdS/CFT, corresponding subsystem entanglement spectrum is flat. This behavior is seemingly in sharp contradiction with the one for the thermal (microcanonical) state, and thus in apparent contradiction with the subsystem Eigenstate Thermalization Hypothesis (ETH). In this work, we resolve this issue by comparing the primary state with the KdV (micro)canonical ensemble. We show that the results are consistent with the KdV-generalized version of the subsystem ETH, in which local properties of quantum eigenstates are governed by their values of conserved KdV charges. Our work solidifies evidence for the KdV-generalized ETH in 2d CFTs and emphasizes Renyi entropy as a sensitive probe of the reduced-density matrix.

hep-th↗

arXiv2024

Dissecting Quantum Many-body Chaos in the Krylov Space

The growth of simple operators is essential for the emergence of chaotic dynamics and quantum thermalization. Recent studies have proposed different measures, including the out-of-time-order correlator and Krylov complexity. It is established that the out-of-time-order correlator serves as the signature of quantum many-body chaos, while the Krylov complexity provides its upper bound. However, there exist non-chaotic systems in which Krylov complexity grows exponentially, indicating that the Krylov complexity itself is not a witness of many-body chaos. In this letter, we introduce the missing ingredient, named as the Krylov metric $K_{mn}$, which probes the size of the Krylov basis. We propose that the universal criteria for fast scramblers include (i) the exponential growth of Krylov complexity, (ii) the diagonal elements $K_{nn}\sim n^h$ with $h\in(0,1]$, and (iii) the negligibility of off-diagonal elements $K_{mn}$ with $m\neq n$. We further show that $h=\varkappa / 2α$ is a ratio between the quantum Lyapunov exponent $\varkappa$ and the Krylov exponent $α$. This proposal is supported by both generic arguments and explicit examples, including solvable SYK models, Luttinger Liquids, and many-body localized systems. Our results provide a refined understanding of how chaotic dynamics emerge from the Krylov space perspective.

quant-ph↗

arXiv2023

Causal shadow and non-local modular flow: from degeneracy to perturbative genesis by correlation

Causal shadows are bulk space-time regions between the entanglement wedges and the causal wedges, their existence encodes deep aspects of the entanglement wedge reconstruction in the context of subregion duality in AdS/CFT. In this paper, we study the perturbation theory of the causal shadows and their relation to the properties of the associated modular flows. We first revisit the cases of degenerate causal shadows based on known examples, and discuss the origin for their degeneracy via the local nature of the modular flow. We then focus on the perturbative case in which the CFT subregion consists of two spheres separated by a large distance $L\gg R_{1,2}$. The RT surfaces still agree with the causal horizons, giving a degenerate causal shadow classically. We compute the corrections to the quantum extremal surfaces (Q.E.S) from the bulk mutual information, which then give rise to a non-degenerate causal shadow at order $G_N$. We end by discussing the causal shadow perturbation theory more generally, in particular we explore the possibility of extracting the positivity conditions characterizing perturbative causal shadows in the boundary CFTs.

hep-th↗

arXiv2022

Shape dependence of mutual information in the OPE limit: linear responses

Mutual information serves as an important measure of correlation between subsystem components. In the framework of quantum field theories (QFTs) they have better regulated UV behavior than entanglement entropy, and thus provide more direct access to universal aspects of entanglement structures. In this paper, we study the linear responses under shape deformation of the mutual information in the conformal field theory (CFT) vacuum between two spheres of radius $R$ separated by large distance $L\gg R$ or conformally equivalent configurations. Our calculations make use of the previous OPE results for mutual information \cite{Faulkner2016Aug} and the associated modular Hamiltonian \cite{Faulkner2021Aug}. In particular, we apply the entanglement first law to compute the linear responses of mutual information under shape deformation on one of the spheres. We find that the linear responses exhibit a high degree of universality for a selected class of OPE contributions. We demonstrate that there is a "little group" of symmetries associated with the set-up. Our result implies that the spherical mutual information is extremal over shape deformations of non-zero modes under the symmetry group.

hep-th↗

arXiv2020

Enhanced corrections near holographic entanglement transitions: a chaotic case study

Recent work found an enhanced correction to the entanglement entropy of a subsystem in a chaotic energy eigenstate. The enhanced correction appears near a phase transition in the entanglement entropy that happens when the subsystem size is half of the entire system size. Here we study the appearance of such enhanced corrections holographically. We show explicitly how to find these corrections in the example of chaotic eigenstates by summing over contributions of all bulk saddle point solutions, including those that break the replica symmetry. With the help of an emergent rotational symmetry, the sum over all saddle points is written in terms of an effective action for cosmic branes. The resulting Renyi and entanglement entropies are then naturally organized in a basis of fixed-area states and can be evaluated directly, showing an enhanced correction near holographic entanglement transitions. We comment on several intriguing features of our tractable example and discuss the implications for finding a convincing derivation of the enhanced corrections in other, more general holographic examples.

hep-th↗

arXiv2019

Barrier from chaos: operator entanglement dynamics of the reduced density matrix

It is believed that thermalization drives the reduced density matrix of a subsystem to approach a short-range entangled operator. If the initial state is also short-range entangled, it is possible that the reduced density matrix remains low-entangled throughout thermalization; or there could exist a barrier with high operator entanglement between the initial and thermalized reduced density matrix. In this paper, we study such dynamics in three classes of models: the rational CFTs, the random unitary circuit, and the holographic CFTs, representing systems of increasing quantum chaoticity. We show that in all three classes of models, the operator entanglement (or variant of) exhibits three phases, a linear growth phase, a plateau phase, and a decay phase. The plateau phase characterized by volume-law operator entanglement corresponds to the barrier in operator entanglement. While it is present in all three models, its persistence and exit show interesting distinctions among them. The rational CFTs have the shortest plateau phase, followed by the slowest decay phase; the holographic CFTs mark the opposite end, i.e. having the longest plateau phase followed by a discontinuous drop; and the random unitary circuit shows the intermediate behavior. We discuss the mechanisms underlying these behaviors in operator entanglement barriers, whose persistence might serve as another measure for quantum chaoticity.

hep-th↗

arXiv2019

A General Proof of the Quantum Null Energy Condition

We prove a conjectured lower bound on $\left< T_{--}(x) \right>_ψ$ in any state $ψ$ of a relativistic QFT dubbed the Quantum Null Energy Condition (QNEC). The bound is given by the second order shape deformation, in the null direction, of the geometric entanglement entropy of an entangling cut passing through $x$. Our proof involves a combination of the two independent methods that were used recently to prove the weaker Averaged Null Energy Condition (ANEC). In particular the properties of modular Hamiltonians under shape deformations for the state $ψ$ play an important role, as do causality considerations. We study the two point function of a "probe" operator $\mathcal{O}$ in the state $ψ$ and use a lightcone limit to evaluate this correlator. Instead of causality in time we consider \emph{causality in modular time} for the modular evolved probe operators, which we constrain using Tomita-Takesaki theory as well as certain generalizations pertaining to the theory of modular inclusions. The QNEC follows from very similar considerations to the derivation of the chaos bound and the causality sum rule. We use a kind of defect Operator Product Expansion to apply the replica trick to these modular flow computations, and the displacement operator plays an important role. Our approach was inspired by the AdS/CFT proof of the QNEC which follows from properties of the Ryu-Takayanagi (RT) surface near the boundary of AdS, combined with the requirement of entanglement wedge nesting. Our methods were, as such, designed as a precise probe of the RT surface close to the boundary of a putative gravitational/stringy dual of \emph{any} QFT with an interacting UV fixed point. We also prove a higher spin version of the QNEC.

hep-th↗

arXiv2019

A modular toolkit for bulk reconstruction

We introduce new tools for studying modular flow in AdS/CFT. These tools allow us to efficiently extract bulk information related to causality and locality. For example, we discuss the relation between analyticity in modular time and entanglement wedge nesting which can then be used to extract the location of the Ryu-Takayanagi (RT) surface directly from the boundary theory. Probing the RT surface close to the boundary our results reduce to the recent proof of the Quantum Null Energy Condition. We focus on heavy probe operators whose correlation functions are determined by spacelike geodesics. These geodesics interplay with the RT surface via a set of rules that we conjecture and give evidence for using the replica trick.

hep-th↗

arXiv2019

Generalized Wen-Zee Terms

Motivated by symmetry-protected topological phases (SPTs) with both spatial symmetry (e.g., lattice rotation) and internal symmetry (e.g., spin rotation), we propose a class of exotic topological terms, which generalize the well-known Wen-Zee topological terms of quantum Hall systems [X.-G. Wen and A. Zee, Phys. Rev. Lett. 69, 953 (1992)]. These generalized Wen-Zee terms are expressed as wedge product of spin connection and usual gauge fields (1-form or higher) in various dimensions. In order to probe SPT orders, we externally insert "symmetry twists" like domain walls of discrete internal symmetry and disclinations that are geometric defects with nontrivial Riemann curvature. Then, generalized Wen-Zee terms simply tells us how SPTs respond to those symmetry twists. Classifying these exotic topological terms thus leads to a complete classification and characterization of SPTs within the present framework. We also propose SPT low-energy field theories, from which generalized Wen-Zee terms are deduced as topological response actions. Following the Abstract of Wen-Zee paper, our work enriches alternative possibilities of condensed-matter realization of unification of electromagnetism and "gravity".

cond-mat.str-el↗

arXiv2018

Probing beyond ETH at large $c$

We study probe corrections to the Eigenstate Thermalization Hypothesis (ETH) in the context of 2D CFTs with large central charge and a sparse spectrum of low dimension operators. In particular, we focus on observables in the form of non-local composite operators $\mathcal{O}_{obs}(x)=\mathcal{O}_L(x)\mathcal{O}_L(0)$ with $h_L\ll c$. As a light probe, $\mathcal{O}_{obs}(x)$ is constrained by ETH and satisfies $\langle \mathcal{O}_{obs}(x)\rangle_{h_H}\approx \langle \mathcal{O}_{obs}(x)\rangle_{\text{micro}}$ for a high energy energy eigenstate $| h_H\rangle$. In the CFTs of interests, $\langle \mathcal{O}_{obs}(x)\rangle_{h_H}$ is related to a Heavy-Heavy-Light-Light (HL) correlator, and can be approximated by the vacuum Virasoro block, which we focus on computing. A sharp consequence of ETH for $\mathcal{O}_{obs}(x)$ is the so called "forbidden singularities", arising from the emergent thermal periodicity in imaginary time. Using the monodromy method, we show that finite probe corrections of the form $\mathcal{O}(h_L/c)$ drastically alter both sides of the ETH equality, replacing each thermal singularity with a pair of branch-cuts. Via the branch-cuts, the vacuum blocks are connected to infinitely many additional "saddles". We discuss and verify how such violent modification in analytic structure leads to a natural guess for the blocks at finite $c$: a series of zeros that condense into branch cuts as $c\to\infty$. We also discuss some interesting evidences connecting these to the Stoke's phenomena, which are non-perturbative $e^{-c}$ effects. As a related aspect of these probe modifications, we also compute the Renyi-entropy $S_n$ in high energy eigenstates on a circle. For subsystems much larger than the thermal length, we obtain a WKB solution to the monodromy problem, and deduce from this the entanglement spectrum.

hep-th↗

arXiv2017

Superconductivity vs quantum criticality: effects of thermal fluctuations

We study the interplay between superconductivity and non-Fermi liquid behavior of a Fermi surface coupled to a massless $SU(N)$ matrix boson near the quantum critical point. The presence of thermal infrared singularities in both the fermionic self-energy and the gap equation invalidates the Eliashberg approximation, and makes the quantum-critical pairing problem qualitatively different from that at zero temperature. Taking the large $N$ limit, we solve the gap equation beyond the Eliashberg approximation, and obtain the superconducting temperature $T_c$ as a function of $N$. Our results show an anomalous scaling between the zero-temperature gap and $T_c$. For $N$ greater than a critical value, we find that $T_c$ vanishes with a Berezinskii-Kosterlitz-Thouless scaling behavior, and the system retains non-Fermi liquid behavior down to zero temperature. This confirms and extends previous renormalization-group analyses done at $T=0$, and provides a controlled example of a naked quantum critical point. We discuss the crucial role of thermal fluctuations in relating our results with earlier work where superconductivity always develops due to the special role of the first Matsubara frequency.

cond-mat.supr-con↗