arXiv subjects

Yongjiang Xu

Publications and source records attributed to Yongjiang Xu.

3 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↗