arXiv subjects

Yueshui Zhang

Publications and source records attributed to Yueshui Zhang.

9 recordsLinked to original sources

arXiv2026

Excited states from local effective Hamiltonians of matrix product states and their entanglement spectrum transition

Solving excited states is a challenging task for interacting systems. For one-dimensional critical systems, however, excited states can be directly accessed from the eigenvectors of the local effective Hamiltonian that is constructed from the ground state obtained by variational matrix product state (MPS) optimization. Despite its numerical success, the theoretical mechanism underlying this method has remained largely unexplored. In this work, we provide a conformal field theory (CFT) perspective that helps elucidate this connection. The key insight is that this construction effectively uses a truncated basis of ground-state Schmidt vectors to represent excited states, where the contribution of each Schmidt vector can be expressed as a CFT correlation function and shown to decay with increasing Schmidt index. The CFT analysis further predicts an entanglement-spectrum transition of excited states as the ratio of the subsystem size to the total system size is varied. Our numerical results support this picture and demonstrate a reorganization of the entanglement spectrum into distinct conformal towers as this ratio changes.

cond-mat.str-el↗

arXiv2026

Crosscap states and duality of Ising field theory in two dimensions

We propose two distinct crosscap states for the two-dimensional (2D) Ising field theory. These two crosscap states, identifying Ising spins or dual spins (domain walls) at antipodal points, are shown to be related via the Kramers-Wannier duality transformation. We derive their Majorana free field representations and extend bosonization techniques to calculate correlation functions of the 2D Ising conformal field theory (CFT) with different crosscap boundaries. Away from criticality, we develop a conformal perturbation theory to calculate the Klein bottle entropy (norm-square of the crosscap overlap) as a universal scaling function [Phys. Rev. Lett. 130, 151602 (2023)]. For the Ising field theory, our analytical results support the conjectured monotonicity of the Klein bottle entropy under relevant perturbations. The formalism provides a general framework for studying perturbed 2D CFTs on non-orientable manifolds.

cond-mat.str-el↗

arXiv2026

SO(n) Affleck-Kennedy-Lieb-Tasaki states as conformal boundary states of integrable SU(n) spin chains

We construct a class of conformal boundary states in the $\mathrm{SU}(n)_1$ Wess-Zumino-Witten (WZW) conformal field theory (CFT) using the symmetry embedding $\mathrm{Spin}(n)_2 \subset \mathrm{SU}(n)_1$. These boundary states are beyond the standard Cardy construction and possess $\mathrm{SO}(n)$ symmetry. The $\mathrm{SU}(n)$ Uimin-Lai-Sutherland (ULS) spin chains, which realize the $\mathrm{SU}(n)_1$ WZW model on the lattice, allow us to identify these boundary states as the ground states of the $\mathrm{SO}(n)$ Affleck-Kennedy-Lieb-Tasaki spin chains. Using the integrability of the $\mathrm{SU}(n)$ ULS model, we analytically compute the corresponding Affleck-Ludwig boundary entropy using exact overlap formulas. Our results unveil intriguing connections between exotic boundary states in CFT and integrable lattice models, thus providing deep insights into the interplay of symmetry, integrability, and boundary critical phenomena.

cond-mat.str-el↗

arXiv2026

Finite-size corrections to the crosscap overlap in the two-dimensional Ising model

We analyze the finite-size corrections to the crosscap overlap in the two-dimensional classical Ising model along its self-dual critical line. Using a fermionic formulation, we express the lattice crosscap overlap in terms of Bogoliubov angles and develop a contour-integral approach by analytically continuing the lattice momentum to the complex plane. This leads to a remarkably simple expression for the crosscap overlap, which demonstrates that the finite-size corrections decay exponentially with system size. We further derive an exact analytical formula for the corresponding decay constant and show that it is determined by the complex singularity structure of the Bogoliubov angle.

cond-mat.stat-mech↗

arXiv2026

Impurity screening by defects in (1+1)$d$ quantum critical systems

We propose a novel mechanism of impurity screening in (1+1)$d$ quantum critical states described by conformal field theories (CFTs). An impurity can be screened if it has the same quantum numbers as some gapless degrees of freedom of the CFT. The common source of these degrees of freedom is the chiral primary fields of the CFT, but we uncover that topological defect lines of the CFT may also take this role. Theoretical analysis relies on the insight that the impurities can be interpreted as edge modes of certain symmetry-protected topological (SPT) states. By stacking a SPT state with a CFT, one or two interfaces on which the SPT edge modes reside are created. If screening occurs due to topological defect lines, a symmetry-enriched CFT with exotic boundary states are obtained. The boundary conditions that appear in these cases are difficult to achieve using previously known methods. As a concrete example, we consider a spin-1 chain whose bulk is described by the SU(3)$_{1}$ CFT and edges are coupled to spin-1/2 impurities. We demonstrate that both the low-energy eigenstates and the extracted Affleck-Ludwig entropy are in excellent agreement with our theoretical predictions.

cond-mat.str-el↗

arXiv2025

Numerical extraction of crosscap coefficients in microscopic models for (2+1)D conformal field theory

Conformal field theory (CFT) can be placed on disparate space-time manifolds to facilitate investigations of their properties. For (2+1)-dimensional [(2+1)D] theories, one useful choice is the real projective space $\mathbb{RP}^3$ obtained by identifying antipodal points on the boundary sphere of a three-dimensional ball. One-point functions of scalar primary fields on this manifold generally do not vanish and encode the so-called crosscap coefficients. These coefficients also manifest on the sphere as the overlaps between certain crosscap states and CFT primary states. Taking the (2+1)D Ising CFT as a concrete example, we demonstrate that crosscap coefficients can be extracted from microscopic models. We construct crosscap states in both lattice models defined on polyhedrons and continuum models in Landau levels, where the degrees of freedom at antipodal points are entangled in Bell-type states. By computing their overlaps with the eigenstates of many-body Hamiltonians, we obtain results consistent with those from conformal bootstrap. Importantly, our approach directly reveals the absolute values of crosscap overlaps, whereas bootstrap calculations typically yield only their ratios. Furthermore, we investigate the finite-size scaling of these overlaps and their evolution under perturbations away from criticality.

hep-th↗

arXiv2025

Truncated Gaussian basis approach for simulating many-body dynamics

We propose a Truncated Gaussian Basis Approach (TGBA) for simulating the dynamics of quantum many-body systems. The approach constructs an effective Hamiltonian within a reduced subspace, spanned by fermionic Gaussian states, and diagonalizes it to obtain approximate eigenstates and eigenenergies. Symmetries can be exploited to perform parallel computation, enabling to simulate systems with much larger sizes. As an example, we compute the dynamic structure factor and study quench dynamics in a non-integrable quantum Ising chain, known as ``$E_8$ magnet''. The mass ratios calculated through the dynamic structure factor show excellent agreement with Zamolodchikov's analytical predictions. For quench dynamics we observe that time-evolving wave functions in the truncated subspace facilitates the simulation of long-time dynamics.

cond-mat.str-el↗

arXiv2025

Extracting the Luttinger parameter from a single wave function

The low-energy physics of Tomonaga-Luttinger liquids (TLLs) is controlled by the Luttinger parameter. We demonstrate that this parameter can be extracted from a single wave function for one-component TLLs with periodic boundary condition. This method relies on the fact that TLLs are described by conformal field theory in which crosscap states can be constructed. The overlaps between the crosscap states and the ground state as well as some excited states are proved to be universal numbers that directly reveal the Luttinger parameter. In microscopic lattice models, crosscap states are formed by putting each pair of antipodal sites into a maximally entangled state. Analytical and numerical calculations are performed in a few representative models to substantiate the conformal field theory prediction. The extracted Luttinger parameters are generally quite accurate in finite-size systems with moderate lengths, so there is no need to perform data fitting and/or finite-size scaling.

cond-mat.str-el↗

arXiv2023

Universal scaling of Klein bottle entropy near conformal critical points

We show that the Klein bottle entropy [Phys. Rev. Lett. 119, 261603 (2017)] for conformal field theories (CFTs) perturbed by a relevant operator is a universal function of the dimensionless coupling constant. The universal scaling of the Klein bottle entropy near criticality provides an efficient approach to extract the scaling dimension of lattice operators via data collapse. As paradigmatic examples, we validate the universal scaling of the Klein bottle entropy for Ising and Z3 parafermion CFTs with various perturbations using numerical simulation with continuous matrix product operator approach.

cond-mat.str-el↗