arXiv subjects

Hong-Hao Tu

Publications and source records attributed to Hong-Hao Tu.

At least 19 recordsLinked to original sources

arXiv2026

A fractional quantum Hall factory on quantum processors: constant-depth preparation of clustered non-Abelian states

Non-Abelian anyons arise as exotic excitations in fractional quantum Hall (FQH) matter and have proved very elusive to realize in conventional platforms. In this work, we show that on a programmable quantum hardware platform, the more exotic FQH excitations are the less costly ones to prepare: clustered non-Abelian FQH states admit parallel quantum preparation circuits whose two-qubit depth is independent of system size, while constructing the more common Abelian Laughlin state requires a sequential circuit chain with linear depth. The centerpiece of this work is our new systematic framework for cataloging possible FQH states and preparing them on quantum circuits at unprecedented scale and variety. Our prepared parafermionic Read--Rezayi $\mathbb{Z}_3$ state holds depth 3 from 8 to 118 qubits, and full root sampling extends to a 154-qubit, 104-electron Read--Rezayi $\mathbb{Z}_4$ state. In all, our demonstrated 18-family catalog of prepared FQH states extends to all 156 qubits of an IBM Heron processor, limited only by existing hardware scale. Measurements on the prepared states recover the expected fractional quasihole charges, with the charge estimator exact in every symmetry-selected shot for the clustered states, and braiding data of the non-Abelian $e/4$ quasihole measured via interferometric extensions. Our work establishes a scalable route to studying FQH physics on quantum processors and opens new avenues for preparing and probing non-Abelian topological matter far beyond the reach of conventional platforms.

cond-mat.str-el↗

arXiv2026

Extracting central charge from ground-state overlaps of spatially deformed Hamiltonians

We show that the conformal anomaly of a $(1+1)$-dimensional conformal field theory can be extracted directly from a ground-state wave-function overlap associated with a spatial conformal deformation. Focusing on the $q$-Möbius deformation, we derive an exact overlap formula between the deformed and undeformed ground states, whose exponent depends only on the central charge. Motivated by this result, we construct a lattice estimator based solely on ground-state overlaps and apply it to representative critical quantum chains and the gapless edge modes of a two-dimensional Chern insulator. Numerical results demonstrate that the resulting overlaps provide a simple and robust probe of the central charge in microscopic models. We further demonstrate that the deformed ground states retain universal geometric structures in their entanglement spectra and entanglement entropies. These results provide a simple wave-function-based route to probing conformal data in critical systems and topological edge modes.

cond-mat.str-el↗

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

Revisiting the $J_1$-$J_2$ Heisenberg Model on a Triangular Lattice: Quasi-Degenerate Ground States and Phase Competition

It is generally believed that the spin-$\tfrac{1}{2}$ triangular-lattice $J_1$-$J_2$ Heisenberg model hosts a quantum spin liquid in the intermediate regime between the $120^\circ$ and stripe ordered phases. Density matrix renormalization group studies on cylinders have consistently found two nearly degenerate ground states, commonly interpreted as distinct topological sectors. Using state-of-the-art matrix product state simulations on YC6 cylinders, we compare the static and dynamical properties of these two sectors at $J_2/J_1 = 0.125$. Noticeable differences appear already in static correlations; moreover, high-resolution dynamical structure factors reveal qualitatively distinct low-energy excitations. These results suggest that the two ground states cannot be understood as merely topologically distinct sectors of a gapped $\mathbb{Z}_2$ spin liquid.

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

Efficient simulation of low-entanglement bosonic Gaussian states in polynomial time

Bosonic Gaussian states are ubiquitous in quantum optics and condensed matter physics. While they are efficiently handled within the Gaussian formalism, sampling requires calculating amplitudes in the boson occupation basis. This step, however, is hindered by a significant bottleneck due to the hafnian. We present an efficient algorithm that converts pure bosonic Gaussian states into matrix product states (MPSs), thereby establishing a versatile tool for probing bosonic Gaussian systems in settings where direct Gaussian-formalism-based calculations become inefficient. Our method combines a Gaussian singular value decomposition with a projected-creation-operator mapping that constructs local MPS tensors without computing hafnians. Benchmarking on covariance matrices from the Jiuzhang 2.0 and Jiuzhang 4.0 Gaussian boson sampling experiments demonstrates substantial speedups over previous tensor-network approaches in the low-entanglement regime relevant to lossy devices. The method provides a scalable classical simulation framework for bosonic Gaussian states with limited entanglement. In this regime, a target accuracy can be achieved with a bond dimension that remains computationally tractable, thereby extending the applicability of MPS-based methods to a broad range of bosonic systems.

quant-ph↗

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

Bridging conformal field theory and parton approaches to SU(n)_k chiral spin liquids

We employ the $\mathrm{SU}(n)_k$ Wess-Zumino-Witten (WZW) model in conformal field theory to construct lattice wave functions in both one and two dimensions. The spins on all lattice sites are chosen to transform under the $\mathrm{SU}(n)$ irreducible representation with a single row and $k$ boxes in the Young tableau. It is demonstrated that the wave functions can be reinterpreted as parton states, which enables efficient conversion to matrix product states such that many physical properties can be evaluated directly. In one dimension, these wave functions describe critical spin chains whose universality classes are in one-to-one correspondence with the WZW models used in the construction. In two dimensions, our constructions yield model wave functions for chiral spin liquids, and we show how to find all topological sectors of them in a systematic way. Using the null vectors of Kac-Moody algebras, parent Hamiltonians of the $\mathrm{SU}(3)_k$ series are derived. The $\mathrm{SU}(3)_k$ chiral spin liquids are lattice analogs of non-Abelian spin-singlet fractional quantum Hall states, and the $k=2$ member hosts Fibonacci anyons.

cond-mat.str-el↗

arXiv2025

A Promising Method for Strongly Correlated Electrons in Two Dimensions: Gutzwiller-Guided Density Matrix Renormalization Group

The study of strongly correlated electron systems remains a fundamental challenge in condensed matter physics, particularly in two-dimensional (2D) systems hosting various exotic phases of matter including quantum spin liquids, unconventional superconductivity, and topological orders. Although Density Matrix Renormalization Group (DMRG) has established itself as a pillar for simulating one-dimensional quantum systems, its application to 2D systems has long been hindered by the notorious ``local minimum'' issues. Recent methodological breakthroughs have addressed this challenge by incorporating Gutzwiller-projected wavefunctions as initial states for DMRG simulations. This hybrid approach, referred to as DMRG guided by Gutzwiller-projected wave functions (or Gutzwiller-guided DMRG), has demonstrated remarkable improvements in accuracy, efficiency, and the ability to explore exotic quantum phases such as topological orders. This review examines the theoretical underpinnings of this approach, details key algorithmic developments, and showcases its applications in recent studies of 2D quantum systems.

cond-mat.str-el↗

arXiv2025

Efficient conversion from fermionic Gaussian states to matrix product states

Fermionic Gaussian states are eigenstates of quadratic Hamiltonians and are widely used in quantum many-body problems. We propose a highly efficient algorithm that converts fermionic Gaussian states to matrix product states. It can be formulated for finite-size systems without translation invariance, but becomes particularly appealing when applied to infinite systems with translation invariance. If the ground states of a topologically ordered system on infinite cylinders are expressed as matrix product states, then the fixed points of the transfer matrix can be harnessed to filter out the anyon eigenbasis, also known as minimally entangled states. This allows for efficient computation of universal properties, such as the entanglement spectrum and modular matrices. The potential of our method is demonstrated by numerical calculations in two chiral spin liquids that have the same topological orders as the bosonic Laughlin and Moore-Read states, respectively. The anyon eigenbasis for the first one has been worked out before and serves as a useful benchmark. The anyon eigenbasis of the second one is, however, not transparent, and its successful construction provides a nontrivial corroboration of our method.

cond-mat.str-el↗

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

Dirac and chiral spin liquids on spin-1/2 square-lattice Heisenberg antiferromagnet

We revisit the challenging problem of identifying the quantum spin liquid candidate in the spin-1/2 $J_1$-$J_2$ Heisenberg antiferromagnet on the square lattice. By integrating the Gutzwiller-guided density matrix renormalization group method with analytical analyses, we present clear evidence that the ground state is a Z$_2$ Dirac spin liquid. This state can be efficiently described by a Gutzwiller-projected parton theory characterized by its projective symmetry group. To distinguish the difference between the projected Z$_2$ and U(1) parton state, we investigate the chiral spin liquid ground states as topological orders by incorporating a $J_χ$ term into the $J_1$-$J_2$ model and observe a transition from a Z$_2$ chiral spin liquid to a U(1)$_2$ chiral spin liquid as $J_χ$ increases.

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↗

arXiv2024

Symmetry-protected topological phases, conformal criticalities, and duality in exactly solvable SO($n$) spin chains

We introduce a family of SO($n$)-symmetric spin chains which generalize the transverse-field Ising chain for $n=1$. These spin chains are defined with Gamma matrices and can be exactly solved by mapping to $n$ species of itinerant Majorana fermions coupled to a static $\mathbb{Z}_2$ gauge field. Their phase diagrams include a critical point described by the $\mathrm{Spin}(n)_{1}$ conformal field theory as well as two distinct gapped phases. We show that one of the gapped phases is a trivial phase and the other realizes a symmetry-protected topological phase when $n \geq 2$. These two gapped phases are proved to be related to each other by a Kramers-Wannier duality. Furthermore, other elegant structures in the transverse-field Ising chain, such as the infinite-dimensional Onsager algebra, also carry over to our models.

cond-mat.str-el↗

arXiv2024

Open Quantum System Dynamics from Infinite Tensor Network Contraction

Approaching the long-time dynamics of non-Markovian open quantum systems presents a challenging task if the bath is strongly coupled. Recent proposals address this problem through a representation of the so-called process tensor in terms of a tensor network. We show that for Gaussian environments highly efficient contraction to matrix product operator (MPO) form can be achieved with infinite MPO evolution methods, leading to significant computational speed-up over existing proposals. The result structurally resembles open system evolution with carefully designed auxiliary degrees of freedom, as in hierarchical or pseudomode methods. Here, however, these degrees of freedom are generated automatically by the MPO evolution algorithm. Moreover, the semi-group form of the resulting propagator enables us to explore steady-state physics, such as phase transitions.

quant-ph↗