arXiv subjects

Wei-Lin Tu

Publications and source records attributed to Wei-Lin Tu.

18 recordsLinked to original sources

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 $120^\circ$ N\'eel 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

Dynamic Moir\'e Potentials and Robust Wigner Crystallization in Large-Scale Twisted Transition Metal Dichalcogenides

Understanding the dynamical evolution of large-scale moir\'e systems is crucial for connecting theoretical predictions with experimental observations. Here we develop a machine-learning-based workflow, integrating DeePMD and DeepH frameworks with first-principles calculations, to efficiently investigate time-dependent structural and electronic responses in twisted bilayer transition metal dichalcogenides (TMDs) with experimentally relevant moir\'e supercells containing over 3000 atoms. Using $\mathrm{WS_2}$ as a representative system, we show that low-temperature lattice vibrations and relaxation deepen the moir\'e potential wells, narrow the lowest conduction band, and facilitate the formation of strongly localized electronic states. Based on DFT-derived moir\'e potentials that incorporate these dynamical effects, density-matrix-renormalization-group (DMRG) simulations reveal robust Wigner crystallization and a kagom\'e-patterned three-electron state, consistent with recent experimental observations. Our workflow provides a practical route for exploring large moir\'e supercells beyond static configurations and offers new insight into the interplay between lattice dynamics, electronic localization, and emergent correlated states in twisted two-dimensional materials.

cond-mat.mtrl-sci↗

arXiv2026

Tensor-Augmented Convolutional Neural Networks: Enhancing Expressivity with Generic Tensor Kernels

Convolutional Neural Networks (CNNs) excel at extracting local features hierarchically, but their performance in capturing complex correlations hinges heavily on deep architectures, which are usually computationally demanding and difficult to interpret. To address these issues, we propose a physically-guided shallow model: tensor-augmented CNN (TACNN), which replaces conventional convolution kernels with generic tensors to enhance representational capacity. This choice is motivated by the fact that an order-$N$ tensor naturally encodes an arbitrary quantum superposition state in the Hilbert space of dimension $d^N$, where $d$ is the local physical dimension, thus offering substantially richer expressivity. Furthermore, in our design the convolution output of each layer becomes a multilinear form capable of capturing high-order feature correlations, thereby equipping a shallow multilayer architecture with an expressive power competitive to that of deep CNNs. On the Fashion-MNIST benchmark, TACNN demonstrates clear advantages over conventional CNNs, achieving remarkable accuracies with only a few layers. In particular, a TACNN with only two convolution layers attains a test accuracy of 93.7$\%$, surpassing or matching considerably deeper models such as VGG-16 (93.5$\%$) and GoogLeNet (93.7$\%$). These findings highlight TACNN as a promising framework that strengthens model expressivity while preserving architectural simplicity, paving the way towards more interpretable and efficient deep learning models.

cs.CV↗

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

Clifford Circuits Augmented Grassmann Matrix Product States

Recent progress in combining Clifford circuits with tensor-network (TN) methods has shown that local Clifford disentanglers can reduce bipartite entanglement across TN bonds prior to tensor compression, thereby improving the efficiency of TN simulations. In this work, we embed local Clifford disentanglers in the Grassmann-tensor language to define a Clifford-augmented Grassmann matrix product state (CAGMPS) ansatz, and develop a density-matrix renormalization group (DMRG) framework based on this ansatz while preserving locality and fermion-parity structure. We benchmark the resulting CAGMPS--DMRG method on representative fermionic lattice systems, including the tight-binding, $t$-$V$, and $t$-$V$-$V'$ models. In all cases, Clifford augmentation systematically suppresses bipartite entanglement and improves the accuracy of the ground-state energy at a fixed bond dimension. We further show that the Grassmann-evenness condition, together with equivalence under entangling action, restricts the relevant two-site Clifford candidates to 12 inequivalent representatives, enabling a more economical disentangling search than approaches based on the standard two-qubit Clifford gate set. Our results suggest that the CAGMPS--DMRG method provides a scalable and efficient variational tool for strongly correlated fermionic systems.

quant-ph↗

arXiv2023

Programmable order by disorder effect and underlying phases through dipolar quantum simulators

In this work, we study two different quantum simulators composed of molecules with dipole-dipole interaction through various theoretical and numerical tools. Our first result provides knowledge upon the quantum order by disorder effect of the $S=1/2$ system, which is programmable in a quantum simulator composed of circular Rydberg atoms in the triangular optical lattice with a controllable diagonal anisotropy. When the numbers of up spins and down spins are equal, a set of sub-extensive degenerate ground states is present in the classical limit, composed of continuous strings whose configuration enjoys a large degree of freedom. Adopting the the real space perturbation theory, our calculation demonstrates a lifting of the degeneracy, favoring the stripe configuration. When $J$ becomes larger, we adopt the infinite projected entangled-pair state~(iPEPS) and numerically check the effect of degeneracy lifting. The iPEPS results show that even when the spin exchange coupling is strong the stripe pattern is still favored. Next, we study the dipolar bosonic model with tilted polar angle which can be realized through a quantum simulator composed of cold atomic gas with dipole-dipole interaction in an optical lattice. By placing the atoms in a triangular lattice and tilting the polar angle, the diagonal anisotropy can also be realized in the bosonic system. With our cluster mean-field theory calculation, we provide various phase diagrams with different tilted angles, showing the abundant underlying phases including the supersolid. Our proposal indicates realizable scenarios through quantum simulators in studying the quantum effect as well as extraordinary phases. We believe that our results indicated here can also become a good benchmark for the two-dimensional quantum simulators.

cond-mat.quant-gas↗

arXiv2023

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↗

arXiv2022

Intertwined Orders and Electronic Structure in Superconducting Vortex Halos

We present a comprehensive study of vortex structures in $d$-wave superconductors from large-scale renormalized mean-field theory of the square-lattice $t$-$t'$-$J$ model, which has been shown to provide a quantitative modeling for high-$T_c$ cuprate superconductors. With an efficient implementation of the kernel polynomial method for solving electronic structures, self-consistent calculations involving up to $10^5$ variational parameters are performed to investigate the vortex solutions on lattices of up to $10^4$ sites. By taking into account the strong correlation of the model, our calculations shed new lights on two puzzling results that have emerged from recent scanning tunneling microscopy (STM) experiments. The first concerns the issue of the zero-biased-conductance peak (ZBCP) at the vortex core for a uniform $d$-wave superconducting state. Despite its theoretical prediction, the ZBCP was not observed in most doping range of cuprates except in heavily over-doped samples at low magnetic field. The second issue is the nature of the checkerboard charge density waves (CDWs) with a period of about 8 unit cells in the vortex halo at optimal doping. Although it has been suggested that such bipartite structure arises from low-energy quasiparticle interference, another intriguing scenario posits that the checkerboard CDWs originate from an underlying bidirectional pair-density wave (PDW) ordering with the same period. We present a coherent interpretation of these experimental results based on systematic studies of the doping and magnetic field effects on vortex solutions with and without a checkerboard structure. The mechanism of the emergent intertwined orders within the vortex halo is also discussed.

cond-mat.supr-con↗

arXiv2022

Variational Tensor Network Operator

We propose a simple and generic construction of the variational tensor network operators to study the quantum spin systems by the synergy of ideas from the imaginary-time evolution and variational optimization of trial wave functions. By applying these operators to simple initial states, accurate variational ground state wave functions with extremely few parameters can be obtained. Furthermore, the framework can be applied to study spontaneously symmetry breaking, symmetry protected topological, and intrinsic topologically ordered phases, and we show that symmetries of the local tensors associated with these phases can emerge directly after the optimization without any gauge fixing. This provides a universal way to identify quantum phase transitions without prior knowledge of the system.

cond-mat.str-el↗

arXiv2022

Cubic ferromagnet and emergent $U(1)$ symmetry on its phase boundary

We study the simplest quantum lattice spin model for the two-dimensional (2D) cubic ferromagnet by means of mean-field analysis and tensor network calculation. While both methods give rise to similar results in detecting related phases, the 2D infinite projected entangled-pair state (iPEPS) calculation provides more accurate values of transition points. Near the phase boundary, moreover, our iPEPS results indicate that it is more difficult to pin down the orientation of magnetic easy axes, and we interpret it as the easy-axis softening. This phenomenon implies an emergence of continuous $U(1)$ symmetry, which is indicated by the low-energy effective model and has been analytically shown by the field theory. Our model and study provide a concrete example for utilizing iPEPS near the critical region, showing that the emergent phenomenon living on the critical points can already be captured by iPEPS with a rather small bond dimension.

cond-mat.str-el↗

arXiv2021

Field-induced Bose-Einstein condensation and supersolid in the two-dimensional Kondo necklace

The application of an external magnetic field of sufficient strength to a spin system composed of a localized singlet can overcome the energy gap and trigger bosonic condensation and so provide an alternative method to realize exotic phases of matter in real materials. Previous research has indicated that a spin Hamiltonian with on-site Kondo coupling may be the effective many-body Hamiltonian for $\text{Ba}_2\text{NiO}_2\text{(AgSe)}_2$ (BNOAS) and here we study such a Hamiltonian using a tensor network ansatz in two dimensions. Our results unveil a phase diagram which indicates the underlying phases of BNOAS. We propose, in response to the possible doping-induced superconductivity of BNOAS, a fermionic model for further investigation. We hope that our discovery can bring up further interest in both theoretical and experimental researches for related nickelate compounds.

cond-mat.mtrl-sci↗

arXiv2021

Generating Function for Tensor Network Diagrammatic Summation

The understanding of complex quantum many-body systems has been vastly boosted by tensor network (TN) methods. Among others, excitation spectrum and long-range interacting systems can be studied using TNs, where one however confronts the intricate summation over an extensive number of tensor diagrams. Here, we introduce a set of generating functions, which encode the diagrammatic summations as leading order series expansion coefficients. Combined with automatic differentiation, the generating function allows us to solve the problem of TN diagrammatic summation. We illustrate this scheme by computing variational excited states and dynamical structure factor of a quantum spin chain, and further investigating entanglement properties of excited states. Extensions to infinite size systems and higher dimension are outlined.

cond-mat.str-el↗

arXiv2020

Competing quantum phases of hard-core boson with tilted dipole-dipole interaction

Different quantum phases of hard-core boson induced by dipole-dipole interaction with varying angles of polarization are discussed in this work. We consider the two most influential leading terms with anisotropy due to the tilted polarization of the on-site boson in the square lattice. To ensure the concreteness of this truncation, we compare our phase diagrams, obtained numerically from cluster mean-field theory (CMFT) and infinite projected entangled-pair state (iPEPS), with that of the long-range interacting model from quantum Monte Carlo. Next, we focus on the case where the azimuthal angle is fixed to $\phi = \pi/4$. Using the mean-field analysis where the quantum spin operators are replaced by $c$-numbers, we aim to search for the underlying phases, especially the supersolid. Our results show a competing scenario mainly between two ordered phases with different sizes of unit cell, where first-order transition takes place in between them. With the help of CMFT and variational iPEPS, the phase boundaries predicted by the mean-field theory are determined more precisely. Our discoveries elucidate the possible underlying supersolid phases which might be seen in the ultracold experiments with strongly dipolar atoms. Moreover, our results indicate that an effective triangular optical lattice can be realized by fine tuning the polarization of dipoles in a square lattice.

cond-mat.quant-gas↗

arXiv2019

Frustration-Induced Supersolid Phases of Extended Bose-Hubbard Model in the Hard-Core Limit

We investigate exotic supersolid phases in the extended Bose-Hubbard model with infinite projected entangled-pair state, numerical exact diagonalization, and mean-field theory. We demonstrate that many different supersolid phases can be generated by changing signs of hopping terms, and the interactions along with the frustration of hopping terms are important to stabilize those supersolid states. We argue the effect of frustration introduced by the competition of hopping terms in the supersolid phases from the mean-field point of view. This helps to give a clearer picture of the background mechanism for underlying superfluid/supersolid states to be formed. With this knowledge, we predict and realize the $d$-wave superfluid, which shares the same pairing symmetry with high-$T_c$ materials, and its extended phases. We believe that our results contribute to preliminary understanding for desired target phases in the real-world experimental systems.

cond-mat.other↗

arXiv2018

Evolution of Pairing Orders between Pseudogap and Superconducting Phases of Cuprate Superconductors

One of the most puzzling problems of high temperature cuprate superconductor is the pseudogap phase(PG) at temperatures above the superconducting transition temperature in the underdoped regime. The PG phase is found by the angle-resolved photoemission spectra(ARPES) to have a gap at some regions in momentum space and a fraction of Fermi surface remained, known as Fermi arcs. The arc turns into a d-wave SC gap with a node below the SC transition temperature. Here, by studying a strongly correlated model at low temperatures, we obtained a phase characterized by two kinds of pairing order parameters with the total momentum of the Cooper pair to be zero and finite. The finite momentum pairing is accompanied with a spatial modulation of pairing order, i.e. a pair density wave (PDW). These PDW phases are intertwined with modulations of charge density and intra-unit cell form factors. The coexistence of the two different pairing orders provides the unique two-gaps like spectra observed by ARPES for superconducting cuprates. As temperature raises, the zero momentum pairing order vanishes while the finite momentum pairing orders are kept, thus Fermi arcs are realized. The calculated quasiparticle spectra has the similar doping and temperature dependence as reported by ARPES and scanning tunneling spectroscopy(STS). The consequence of breaking symmetry between x and y due to the unidirectional PDW and the possibility to probe such a PDW state in the PG phase is discussed.

cond-mat.str-el↗

arXiv2017

Competing orders in the Hofstadter t-J model

The Hofstadter model describes non-interacting fermions on a lattice in the presence of an external magnetic field. Motivated by the plethora of solid-state phases emerging from electron interactions, we consider an interacting version of the Hofstadter model including a Hubbard repulsion U. We investigate this model in the large-U limit corresponding to a t-J Hamiltonian with an external (orbital) magnetic field. By using renormalized mean field theory supplemented by exact diagonalization calculations of small clusters, we find evidence for competing symmetry-breaking phases, exhibiting (possibly co-existing) charge, bond and superconducting orders. Topological properties of the states are also investigated and some of our results are compared to related experiments involving ultra-cold atoms loaded on optical lattices in the presence of a synthetic gauge field.

cond-mat.str-el↗

arXiv2016

Incommensurate charge ordered states in the $\mathit{t-t^{\prime}-J}$ model

We study the incommensurate charge ordered states in the $\mathit{t-t^{\prime}-J}$ model using the Gutzwiller mean field theory on large systems. In particular, we explore the properties of incommensurate charge modulated states referred to as nodal pair density waves (nPDW) in the literature. nPDW states intertwine site and bond charge order with modulated $d$-wave pair order, and are characterized by a nonzero amplitude of uniform pairing; they also manifest a dominant intra-unit cell $d$-density wave form factor. To compare with a recent scanning tunneling microscopy (STM) study [Hamidian \textit{et al.}, Nat. Phys. 3519 (2015)] of the cuprate superconductor BSCCO-2212, we compute the continuum local density of states (LDOS) at a typical STM tip height using the Wannier function based approach. By Fourier transforming Cu and O sub-lattice LDOS we also obtain bias-dependent intra-unit cell form factors and spatial phase difference. We find that in the nPDW state the behavior of form factors and spatial phase difference as a function of energy agrees remarkably well with the experiment. This is in contrast to commensurate charge modulated states, which we show do not agree with experiment. We propose that the nPDW states are good candidates for the charge density wave phase observed in the superconducting state of underdoped cuprates.

cond-mat.supr-con↗

arXiv2015

Genesis of charge orders in high temperature superconductors

One of the most puzzling facts about cuprate high-temperature superconductors in the lightly doped regime is the coexistence of uniform superconductivity and/or antiferromagnetism with many low-energy charge-ordered states in a unidirectional charge density wave or a bidirectional checkerboard structure. Recent experiments have discovered that these charge density waves exhibit different symmetries in their intra-unit-cell form factors for different cuprate families. Using a renormalized mean-field theory for a well-known, strongly correlated model of cuprates, we obtain a number of charge-ordered states with nearly degenerate energies without invoking special features of the Fermi surface. All of these self-consistent solutions have a pair density wave intertwined with a charge density wave and sometimes a spin density wave. Most of these states vanish in the underdoped regime, except for one with a large d-form factor that vanishes at approximately 19% doping of the holes, as reported by experiments. Furthermore, these states could be modified to have a global superconducting order, with a nodal-like density of states at low energy.

cond-mat.str-el↗