arXiv subjects

Ji-Yao Chen

Publications and source records attributed to Ji-Yao Chen.

At least 19 recordsLinked to original sources

arXiv2026

Measurement-enhanced entanglement in a monitored superconducting chain

A common view in monitored quantum dynamics is that local measurements suppress entanglement growth. We show that this intuition can fail in a one-dimensional spinful fermionic chain governed by a BCS Hamiltonian with pairing strength $Δ$ and subject to continuous, on-site, spin-resolved charge measurements at rate $γ$. Using free-fermion simulations and quasiparticle analysis, we show that pairing suppresses entanglement growth, while measurements suppress pairing. Their competition yields measurement-enhanced entanglement: for $Δ>0$, the steady-state entanglement $\mathcal{S}_s$ increases with $γ$ over a finite interval $0<γ<γ_{\mathrm{peak}}$. This occurs because stronger measurements suppress pairing correlations, which would otherwise suppress entanglement growth. Using a nonlinear sigma-model calculation and free-fermion simulations, we provide evidence that for $Δ>0$ and small but finite $γ$, the steady-state entanglement scales as $\mathcal{S}_s(L)\sim \ln^2 L$. This implies that, in this setting, measurement-enhanced entanglement does not persist in the thermodynamic limit.

quant-ph↗

arXiv2026

Chiral Edge Excitations of $ν=1/2$ Fractional Chern Insulators in the Bosonic Hofstadter Model

Edge excitations are the defining signature of chiral topologically ordered systems. In continuum fractional quantum Hall (FQH) states, these excitations are described by the chiral Luttinger liquid ($χ$LL) theory. Whether these field theory predictions can be precisely identified in discrete lattice systems of finite width, however, remains a longstanding question. Here we numerically demonstrate that the charge-one edge spectral function of a $ν=1/2$ FCI on an infinitely long strip with width $L_y=10$ quantitatively follows the predictions of $χ$LL theory. The edge spectrum is gapless, chiral, and linear, with spectral weight increasing linearly with both momentum and energy. We further analyze the influence of lattice size, particle number, trapping potential, and charge sector of excitations on the edge properties. Our results establish a clear correspondence between lattice FCIs and continuum FQH systems and provide guidance for future experimental detection of chiral edge modes.

cond-mat.str-el↗

arXiv2026

Investigation of the $J_1$-$J_2$ Heisenberg model on the triangular lattice: A study with projected entangled-pair states

The nature of the quantum spin liquid (QSL) phase in the frustrated $J_1$-$J_2$ Heisenberg model on the triangular lattice remains an open and actively debated problem. In this work, we employ the infinite projected entangled-pair state (PEPS) to systematically investigate the model under different symmetry constraints. Our simulations reveal a direct transition from the $120^\circ$ Néel state to a putative QSL at $J_2/J_1\approx 0.08$, signaled by the collapse of magnetic order. We further show that, through either an appropriate unitary rotation or spontaneous spin long-range order, the stripe antiferromagnetic phase can also be accurately captured within the infinite PEPS framework. A central focus of our study is the role played by the PEPS symmetry in approximating the QSL ground-state sandwiched between the two magnetic phases. We first found that a fully-symmetric topological $\mathbb{Z}_2$ Resonating Valence Bond state, which can be written as a simple PEPS with bond dimension $D=3$, exhibits a reasonably good variational energy. Motivated by this finding, we have further constructed generic $\mathbb{Z}_2$-symmetric PEPS of larger bond dimension (up to $D=7$). We found that, under wavefunction optimization, spinons condense and, simultaneously, topological vison excitations get confined, hence precluding $\mathbb{Z}_2$ topological order. This strongly indicates the gapless (or critical) nature of the QSL phase, which is most naturally consistent with a U(1) Dirac spin liquid scenario.

cond-mat.str-el↗

arXiv2026

Tangent Space Excitation Ansatz for Quantum Circuits

Computing excitation spectra of quantum many-body systems is a promising avenue to demonstrate the practical utility of current noisy quantum devices, especially as we move toward the ``megaquop'' regime. For this task, here we introduce a \textit{tangent space excitation ansatz} for quantum circuits, motivated by the quasi-particle picture of many-body systems and the structural similarity between quantum circuits and tensor networks. Increasing circuit depth by one layer to construct tangent space around the variational optimum of a parametrized quantum circuit, we show that massive low-energy single-particle states can be captured. Our ansatz relies on a distinct mechanism from that of excitation ansatz in matrix product state and projected entangled-pair state, and avoids intrinsic limitations of the latter. Comparing our approach with existing quantum excited-state algorithms, we find that with similar computational cost, both the number of excited states and accuracy are significantly improved. We demonstrate our ansatz in both one and two dimensions, and further show that this approach, implementable using Hadamard test, is scalable and suitable for current quantum processors.

quant-ph↗

arXiv2026

Variational preparation and characterization of chiral spin liquids in quantum circuits

Quantum circuits have been shown to be a fertile ground for realizing long-range entangled phases of matter. While various quantum double models with non-chiral topological order have been theoretically investigated and experimentally implemented, the realization and characterization of chiral topological phases have remained less explored. Here we show that chiral topological phases in spin systems, i.e., chiral spin liquids, can be prepared in quantum circuits using the variational quantum eigensolver (VQE) framework. On top of the VQE ground state, signatures of the chiral topological order are revealed using the recently proposed tangent space excitation ansatz for quantum circuits. We show that, both topological ground state degeneracy and the chiral edge mode can be faithfully captured by this approach. We demonstrate our approach using the Kitaev honeycomb model, finding excellent agreement of low-energy excitation spectrum on quantum circuits with exact solution in all topological sectors. Further applying this approach to a non-exactly solvable chiral spin liquid model on square lattice, the results suggest this approach works well even when the topological sectors are not exactly known.

cond-mat.str-el↗

arXiv2026

Probing the Dynamical Structure Factor of Quantum Spin Chains via Low-Temperature Gibbs States with Matrix Product State Subspace Expansion

Studying finite-temperature properties with tensor networks is notoriously difficult, especially at low temperatures, due to the rapid growth of entanglement and the complexity of thermal states. Existing methods like purification and minimally entangled typical thermal states offer partial solutions but struggle with scalability and accuracy in low-temperature regime. To overcome these limitations, we propose a new approach based on generating-function matrix product states (GFMPS). By directly computing a large set of Bloch-type excited states, we construct Gibbs states that moderate the area-law constraint, enabling accurate and efficient approximation of low-temperature thermal behavior. Our benchmark results show magnificent agreement with both exact diagonalization and experimental observations, validating the accuracy of our approach. This method offers a promising new direction for overcoming the longstanding challenges of studying low-temperature properties within the tensor network framework. We also expect that our method will facilitate the numerical simulation of quantum materials in comparison with experimental observations.

cond-mat.str-el↗

arXiv2025

Simulating Bulk Gap in Chiral Projected Entangled-Pair States

Projected entangled-pair states (PEPS) have proven effective in capturing chiral spin liquid ground states, yet the presence of long-range ``gossamer'' correlation tails raises concerns about their ability to accurately describe bulk gaps. Here, we address this challenge and demonstrate that PEPS can reliably characterize gapped bulk excitations in chiral topological phases. Using a variational principle for excited states within a local mode approximation, we establish that correlation functions decaying faster than $r^{-2}$ are not necessarily related to gapless modes and thus long-range ``gossamer'' correlation tails in chiral PEPS do not contradict the presence of a bulk gap. This framework is validated in the spin-$\frac{1}{2}$ Kitaev model with a chiral term, where PEPS yields excitation gaps that agree well with exact solutions. Extending our approach to the $\mathbb{Z}_3$ Kitaev model, we present compelling evidence for its chiral ground state and accurately resolve its gapped excitations. These findings thus solidify PEPS as a powerful tool for studying both ground and excited states in chiral topological systems, thereby bridging a key gap in the understanding of their bulk properties.

cond-mat.str-el↗

arXiv2024

Entanglement Spectrum as a diagnostic of chirality of Topological Spin Liquids: Analysis of an $\mathrm{SU}(3)$ PEPS

We address the key question of representation of chiral topological quantum states in (2+1) dimensions (i.e., with non-zero chiral central charge) by Projected Entangled Pair States (PEPS). A noted result (due to Wahl, Tu, Schuch, and Cirac [Phys. Rev. Lett. 111, 236805 (2013)], and Dubail and Read [Phys. Rev. B 92, 205307 (2015)]) says that this is possible for non-interacting fermions, but the answer is as yet unknown for interacting systems. Characteristic counting of degeneracies of low-lying states in the entanglement spectrum (ES) at fixed transverse momentum of bipartitioned long cylinders ("Li-Haldane counting") provides often-used supporting evidence for chirality. However, non-chiral PEPS (with zero chiral central charge), yet with strong breaking of time-reversal and reflection symmetries, with invariance under the product of these two operations (i.e., "apparently" chiral states), are known whose low-lying ES exhibits the same Li-Haldane counting as a chiral state in certain topological sectors [Kurečić, Vanderstraeten, and Schuch, Phys. Rev. B 99, 045116 (2019); Arildsen, Schuch, and Ludwig, Phys. Rev. B 108, 245150 (2023)]. In the present work, we identify a distinct indicator and hallmark of chirality in the ES of PEPS with global $\mathrm{SU}(3)$ symmetry: the splittings of conjugate irreps. We prove that in the ES of the chiral states conjugate irreps are exactly degenerate, because the operators that would split them [related to the cubic Casimir invariant of $\mathrm{SU}(3)$] are forbidden. By contrast, in the ES of non-chiral states, conjugate splittings are demonstrably non-vanishing. Such a diagnostic provides an unambiguous and powerful tool to distinguish chiral and non-chiral topological states in (2+1) dimensions via their entanglement spectra.

cond-mat.str-el↗

arXiv2024

Fractional Chern insulator candidate in twisted bilayer checkboard lattice

We investigate a fractional Chern insulator (FCI) candidate arising from Moiré bands with higher Chern number C=2 on a magic angle twisted bilayer checkboard lattice (MATBCB). There are two nearly flat low lying bands in the single particle energy spectrum under the first magic angle $ϕ\approx 1.608^{\circ}$ and chiral limit. We find MATBCB hosts a nearly uniform Berry curvature distribution and exhibits tiny violation of quantum geometric trace condition in the first moiré Brillourin Zone (mBZ), indicating that there is a nearly ideal quantum geometry in MATBCB in single particle level. Turning on projected Coulomb interactions, we perform exact diagonalization and find a ten-fold ground state quasi-degeneracy in many body energy spectrum with filling fraction $ν=1/5$. The ten-fold quasi-degenrate ground states further show spectra flow under flux pumping. By diagnosing the particle entanglement spectrum (PES) of the ground states, we obtain a clear PES gap and quasi-hole state counting consistent with Halperin spin singlet generalized Pauli principle, suggesting that a fractional Chern insulator is realized in this system.

cond-mat.str-el↗

arXiv2024

Gauge symmetry of excited states in projected entangled-pair state simulations

While gauge symmetry is a well-established requirement for representing topological orders in projected entangled-pair state (PEPS), its impact on the properties of low-lying excited states remains relatively unexplored. Here we perform PEPS simulations of low-energy dynamics in the Kitaev honeycomb model, which supports fractionalized gauge flux (vison) excitations. We identify gauge symmetry emerging upon optimizing an unbiased PEPS ground state. Using the PEPS adapted local mode approximation, we further classify the low-lying excited states by discerning different vison sectors. Our simulations of spin and spin-dimer dynamical correlations establish close connections with experimental observations. Notably, the selection rule imposed by the locally conserved visons results in nearly flat dispersions in momentum space for excited states belonging to the 2-vison or 4-vison sectors.

cond-mat.str-el↗

arXiv2024

Chiral spin liquid in a generalized Kitaev honeycomb model with $\mathbb{Z}_4$ 1-form symmetry

We explore a large $N$ generalization of the Kitaev model on the honeycomb lattice with a simple nearest-neighbor interacting Hamiltonian. In particular, we focus on the $\mathbb{Z}_4$ case with isotropic couplings, which is characterized by an exact $\mathbb{Z}_4$ one-form symmetry. Guided by symmetry considerations and an analytical study in the single chain limit, on the infinitely long cylinders, we find the model is gapped with an extremely short correlation length. Combined with the $\mathbb{Z}_4$ one-form symmetry, this suggests the model is topologically ordered. To pin down the nature of this phase, we further study the model on both finite and infinitely long strips, where we consistently find a $c=1$ conformal field theory (CFT) description, suggesting the existence of chiral edge modes described by a free boson CFT. Further evidence is found by studying the dimer correlators on infinitely long strips. We find the dimer correlation functions show a power-law decay with the exponent close to 2 on the boundary of the strip, while decay much faster in the bulk. Combined with the topological entanglement entropy extracted from cylinder geometry, we identify the spin liquid is chiral and supports a $\mathrm{U}(1)_{-8}$ chiral topological order. A unified perspective for all $\mathbb{Z}_N$ type Kitaev models is also discussed.

cond-mat.str-el↗

arXiv2024

1-Form Symmetric Projected Entangled-Pair States

The 1-form symmetry, manifesting as loop-like symmetries, has gained prominence in the study of quantum phases, deepening our understanding of symmetry. However, the role of 1-form symmetries in Projected Entangled-Pair States (PEPS), two-dimensional tensor network states, remains largely underexplored. We present a novel framework for understanding 1-form symmetries within tensor networks, specifically focusing on the derivation of algebraic relations for symmetry matrices on the PEPS virtual legs. Our results reveal that 1-form symmetries impose stringent constraints on tensor network representations, leading to distinct anomalous braiding phases carried by symmetry matrices. We demonstrate how these symmetries influence the ground state and tangent space in PEPS, providing new insights into their physical implications for enhancing ground state optimization efficiency and characterizing the 1-form symmetry structure in excited states.

cond-mat.str-el↗

arXiv2024

Robustness of critical U(1) spin liquids and emergent symmetries in tensor networks

We study the response of critical Resonating Valence Bond (RVB) spin liquids to doping with longer-range singlets, and more generally of U(1)-symmetric tensor networks to non-symmetric perturbations. Using a field theory description, we find that in the RVB, doping constitutes a relevant perturbation which immediately opens up a gap, contrary to previous observations. Our analysis predicts a very large correlation length even at significant doping, which we verify using high-accuracy numerical simulations. This emphasizes the need for careful analysis, but also justifies the use of such states as a variational ansatz for critical systems. Finally, we give an example of a PEPS where non-symmetric perturbations do not open up a gap and the U(1) symmetry re-emerges.

cond-mat.str-el↗

arXiv2024

Chiral spin liquid in a $\mathbb{Z}_3$ Kitaev model

We study a $\mathbb{Z}_3$ Kitaev model on the honeycomb lattice with nearest neighbor interactions. Based on matrix product state simulations and symmetry considerations, we find evidence that, with ferromagnetic isotropic couplings, the model realizes a chiral spin liquid, characterized by a possible $\mathrm{U}(1)_{12}$ chiral topological order. This is supported by simulations on both cylinder and strip geometries. On infinitely long cylinders with various widths, scaling analysis of entanglement entropy and maximal correlation length suggests that the model has a gapped 2D bulk. The topological entanglement entropy is extracted and found to be in agreement with the $\mathrm{U}(1)_{12}$ topological order. On infinitely long strips with moderate widths, we find the model is critical with a central charge consistent with the chiral edge theory of the $\mathrm{U}(1)_{12}$ topological phase. We conclude by discussing several open questions.

cond-mat.str-el↗

arXiv2024

Generating function for projected entangled-pair states

Diagrammatic summation is a common bottleneck in modern applications of projected entangled-pair states, especially in computing low-energy excitations of a two-dimensional quantum many-body system. To solve this problem, here we extend the generating function approach for tensor network diagrammatic summation, a scheme previously proposed in the context of matrix product states. Taking the form of a one-particle excitation, we show that the excited state can be computed efficiently in the generating function formalism, which can further be used in evaluating the dynamical structure factor of the system. Our benchmark results for the spin-$1/2$ transverse-field Ising model and Heisenberg model on the square lattice provide a desirable accuracy, showing good agreement with known results. We then study the spin-$1/2$ $J_1$-$J_2$ model on the same lattice and investigate the dynamical properties of the putative gapless spin liquid phase. We conclude with a discussion on generalizations to multi-particle excitations.

cond-mat.str-el↗

arXiv2023

Phase diagram of the chiral SU(3) antiferromagnet on the kagome lattice

Motivated by the search for chiral spin liquids (CSL), we consider a simple model defined on the kagome lattice of interacting SU(3) spins (in the fundamental representation) including two-site and three-site permutations between nearest neighbor sites and on triangles, respectively. By combining analytical developments and various numerical techniques, namely exact Lanczos diagonalizations and tensor network variational approaches, we find a rich phase diagram with non-topological (``trivial") and topological (possibly chiral) gapped spin liquids (SLs). Trivial spin liquids include an Affleck-Kennedy-Lieb-Tasaki (AKLT)-like phase and a trimerized phase, the latter breaking the inversion center between the up and down triangles of the kagome lattice. A topological SL is stabilized in a restricted part of the phase diagram by the time-reversal symmetry breaking (complex) 3-site permutation term. Analyzing the chiral edge modes of this topological SL on long cylinders or on finite disks, we have come up with two competing scenarios, either a CSL or a double Chern-Simon SL characterized by a single or by two counter-propagating Wess-Zumino-Witten SU(3)$_1$ chiral mode(s), respectively. In the vicinity of the extended ferromagnetic region we have found a magnetic phase corresponding either to a modulated canted ferromagnet or to a uniform partially magnetized ferromagnet.

cond-mat.str-el↗

arXiv2023

Chiral spin liquids with projected Gaussian fermionic entangled pair states

We study the parton construction of chiral spin liquids (CSLs) using projected Gaussian fermionic entangled pair states (GfPEPSs). First, we show that GfPEPSs can represent generic spinless Chern insulators faithfully with finite bond dimensions. Then, by applying the Gutzwiller projection to a bi-layer GfPEPSs, spin-1/2 Abelian and non-Abelian CSLs are obtained for Chern number $C=1$ and $C=2$, respectively. As a consequence of the topological obstruction for GfPEPSs, very weak Gossamer tails are observed in the correlation functions of the fermionic projected entangled pair state (PEPS) ansatze, suggesting that the no-go theorem for chiral PEPS is universal but does not bring any practical limitation. Remarkably, without fine tuning, all topological sectors can be constructed showing the expected number of chiral branches in the respective entanglement spectra, providing a sharp improvement with respect to the known bosonic PEPS approach.

cond-mat.str-el↗

arXiv2023

Topological fracton quantum phase transitions by tuning exact tensor network states

Gapped fracton phases of matter generalize the concept of topological order and broaden our fundamental understanding of entanglement in quantum many-body systems. However, their analytical or numerical description beyond exactly solvable models remains a formidable challenge. Here we employ an exact 3D quantum tensor-network approach that allows us to study a $\mathbb{Z}_N$ generalization of the prototypical X cube fracton model and its quantum phase transitions between distinct topological states via fully tractable wavefunction deformations. We map the (deformed) quantum states exactly to a combination of a classical lattice gauge theory and a plaquette clock model, and employ numerical techniques to calculate various entanglement order parameters. For the $\mathbb{Z}_N$ model we find a family of (weakly) first-order fracton confinement transitions that in the limit of $N\to\infty$ converge to a continuous phase transition beyond the Landau-Ginzburg-Wilson paradigm. We also discover a line of 3D conformal quantum critical points (with critical magnetic flux loop fluctuations) which, in the $N\to\infty$ limit, appears to coexist with a gapless deconfined fracton state.

cond-mat.str-el↗