arXiv subjects

Xiao Yan Xu

Publications and source records attributed to Xiao Yan Xu.

At least 19 recordsLinked to original sources

arXiv2026

Stabilizer-Rényi Microscopy of Critical Correlations in Interacting Fermions

Quantum magic---the resource that separates universal quantum computation from efficiently simulable Clifford circuits---has emerged as a diagnostic of many-body quantum states, yet the stabilizer Rényi entropy (SRE) that quantifies it remains largely inaccessible in interacting fermion systems. Estimating the global SRE requires a sum over exponentially many Majorana strings, which in determinant quantum Monte Carlo can be sampled without a sign problem only for the interacting density matrix obtained after averaging the auxiliary fields: sampling strings and fields simultaneously incurs a sign problem even for sign-problem-free models, so that the known sign-free alternative is a nested Monte Carlo that does not scale. We propose instead the two-point SRE---a practical stabilizer-Rényi correlator built from rank-2 SREs of one- and two-site reduced density matrices, which are fixed exactly by single-particle Green functions and density correlations already measured in standard simulations---and show that it obeys universal finite-size scaling at fermionic quantum critical points. In the one-dimensional half-filled spinless $t$-$V$ chain, the correlator distinguishes algebraic and exponential decay regimes and tracks the inverse-logarithmic finite-size drift characteristic of the Berezinskii--Kosterlitz--Thouless transition. On the honeycomb lattice, sign-problem-free quantum Monte Carlo yields Gross--Neveu--Ising scaling with finite anomalous dimension at zero temperature and two-dimensional Ising collapse at the thermal transition. Our results suggest stabilizer-Rényi microscopy as a spatially resolved, quantitatively universal probe of critical correlations in interacting fermionic matter, on par with conventional order-parameter correlators and accessible to quantum-simulator measurements.

cond-mat.str-el↗

arXiv2026

Symmetric Mass Generation in a Bilayer Honeycomb Lattice with $\mathrm{SU}(2)\times\mathrm{SU}(2)\times\mathrm{SU}(2)/\mathbb{Z}_2$ Symmetry

A central question beyond the Landau paradigm is the non-perturbative critical theory of the symmetric mass generation (SMG) transition, where strong interactions gap Dirac fermions in (2+1) dimensions without triggering spontaneous symmetry breaking or topological order. While previous studies have already provided evidence for direct SMG transitions in (2+1) dimensions, the fermion scaling dimension -- the key observable for distinguishing candidate critical theories -- has not been determined in a controlled unbiased way. In this Letter, using large-scale determinant quantum Monte Carlo (DQMC) simulations of a bilayer honeycomb lattice model with $\mathrm{SU}(2)\times\mathrm{SU}(2)\times\mathrm{SU}(2)/\mathbb{Z}_2$ symmetry, we establish a direct continuous transition by observing the simultaneous opening of single-particle and bosonic gaps at a critical coupling $J_c \approx 2.6$ with correlation length exponent $ν= 1.14(2)$, while an exhaustive search over all 19 symmetry-inequivalent fermion bilinear order parameters confirms the absence of any symmetry breaking. We further obtain the first controlled unbiased estimate of the fermion anomalous dimension, $η_ψ= 0.071(1)$, which deviates significantly from the large-$N$ prediction ($η_ψ\approx 0.595$) and variational Monte Carlo estimates ($η_ψ\approx 0.62$), thereby placing direct quantitative constraints on SMG criticality. By contrasting with a related $\mathrm{Spin}(5)\times\mathrm{U}(1)/\mathbb{Z}_2$ model that develops an intermediate excitonic phase, we show that pure non-Abelian symmetry plays a decisive role in stabilizing the direct SMG transition.

cond-mat.str-el↗

arXiv2026

Continuous symmetry analysis and systematic identification of candidate order parameters for interacting fermion models

Symmetry plays a central role in modern physics, from classifying quantum states to characterizing phases of matter through spontaneous symmetry breaking. In interacting fermionic systems with multiple internal degrees of freedom, however, determining the full continuous symmetry group and classifying possible order parameters remain challenging. In this work, we present a systematic framework for analyzing continuous symmetries and identifying candidate order parameters in such systems. By mapping the Hamiltonian to a Majorana representation, we obtain the generators of continuous symmetries from the Lie algebra of operators that commute with the Hamiltonian. We then identify the structure of this Lie algebra using the theory of semisimple Lie algebras. Building on representation theory, we further develop a systematic method for exhaustively enumerating candidate order parameters. By decomposing the exterior-power representations induced by the symmetry algebra on the Majorana space and incorporating discrete lattice symmetries, we classify these order parameters according to the symmetries they break. (Abridged. Please see the PDF manuscript for the complete abstract and specific model applications.)

cond-mat.str-el↗

arXiv2026

Resolving Quantum Criticality in the Honeycomb Hubbard Model

Quantum phase transitions driven by electronic correlations are central to understanding the physics of graphene and related two-dimensional materials. A paradigmatic example is the semimetal-to-Mott-insulator transition on the honeycomb lattice, governed by the Gross-Neveu-Heisenberg universality class, yet consensus on its critical exponents has remained elusive for over a decade due to severe finite-size effects and the absence of rigorous conformal bootstrap benchmarks. Here we try to resolve this long-standing controversy by performing projector determinant quantum Monte Carlo simulations on lattices of unprecedented size, reaching 10,368 sites. By developing a novel projected submatrix update algorithm, we achieve a significant algorithmic speedup that enables us to access the thermodynamic limit with high precision. We observe that the fermion anomalous dimension and the correlation length exponent converge rapidly, while the boson anomalous dimension exhibits a systematic size dependence that we resolve via linear extrapolation. To validate our analysis, we perform parallel large-scale simulations of the spinless $t$-$V$ model on the honeycomb lattice, which belongs to the Gross-Neveu-Ising class. Our results for the $t$-$V$ model show agreement with conformal bootstrap predictions, thereby corroborating the robustness of our methodology. Our work provides state-of-the-art critical exponents for the honeycomb Hubbard model and establishes a systematic finite-size scaling workflow applicable to a broad class of strongly correlated quantum systems, paving the way for resolving other challenging fermionic quantum critical phenomena.

cond-mat.str-el↗

arXiv2026

Linear Canonical-Ensemble Quantum Monte Carlo: From Dilute Fermi Gas to Flat-Band Ferromagnetism

We present a finite-temperature canonical-ensemble determinant quantum Monte Carlo algorithm that enforces an exact fermion number and enables stable simulations of correlated lattice fermions. We propose a stabilized QR update that reduces the computational complexity from standard cubic scaling $O(βN^3)$ to linear scaling $O(βN N_e^2)$ with respect to the system size $N$, where $N_e$ is the particle number. This yields a dramatic speedup in dilute regimes ($N_e \ll N$), opening unbiased access to large-scale simulations of strongly correlated low-density phases. We validate the method on the dilute Fermi gas with onsite Hubbard interactions, observing the suppression of the fermion sign problem in the dilute limit. Furthermore, we apply this approach to an one-dimensional flat-band system, where the canonical ensemble allows for precise control over filling. We reveal a ferromagnetic instability at low temperatures in the half-filling regime. Our linear-scaling approach provides a powerful tool for investigating emergent phenomena in dilute quantum matter.

cond-mat.str-el↗

arXiv2026

The interplay of phase fluctuations and nodal quasiparticles: ubiquitous Fermi arcs in two-dimensional d-wave superconductors

We propose that the pseudogap and Fermi arcs can universally emerge due to thermal (static) phase fluctuations in the normal state of 2D nodal superconductors. By considering a minimal phenomenological model with spatially fluctuating superconducting pairings, we theoretically investigate the role of superconducting phase fluctuations in generic 2D superconductors with disorder-average technique. It is shown for nodal d-wave superconductors that phase fluctuations mediate the scattering of d-wave quasiparticles, smearing out the nodal quasiparticle gap and further leading to pseudogap and Fermi arcs. Moreover, the evolution of Fermi arcs is quantitatively described by two emergent characteristic length scales of the system: one is the finite superconducting correlation length $ξ(T)$, and another the nodal BCS coherence length $ξ_\text{BCS}(k)$. To support our theoretical findings, we numerically report the observation of Fermi arcs in a Hubbard-like model, proposed originally by X. Y. Xu and T. Grover in Phys. Rev. Lett. $\textbf{126}$, 217002 (2021), with sign-problem-free determinant quantum Monte Carlo (DQMC) calculations. As far as we noticed, it is the first time in a correlated model that phase-fluctuating Fermi arcs are identified with unbiased simulations. The numerical results for the scattering rate $Γ_\text{pf}$ of Cooper pairs exhibit excellent agreements with our theoretical predictions, where $Γ_\text{pf}$ is expected to scale linearly with the inverse superconducting correlation length $ξ(T)^{-1}$. This convergence of theory and numerics thereby strongly validates the universal connection between phase fluctuations and Fermi arcs in 2D nodal superconductors.

cond-mat.supr-con↗

arXiv2025

Tunable Luttinger liquid and correlated insulating states in one-dimensional moiré superlattices

Two-dimensional moiré superlattices have been extensively studied, and a variety of correlated phenomena have been observed. However, their lower-dimensional counterpart, one-dimensional (1D) moiré superlattices, remain largely unexplored. Electrons in 1D are generally described by Luttinger liquid theory, with universal scaling relations depending only on the Luttinger parameter g. In particular, at half-filling, Umklapp scattering plays a crucial role, as it can significantly change the conductance-temperature scaling relation and lead to Mott insulators. However, this prediction has never been observed since doping an empty band to half-filling was extremely difficult. Here, we show that the marriage of moiré superlattices and 1D electrons makes it possible to study the Luttinger liquid in an exceptionally wide filling region simply by electrical gating. We perform transport measurements on 1D moiré superlattices of carbon nanotubes on hexagonal boron nitride (hBN) substrates, and observe correlated insulating states at 1/4 and 1/2 fillings of the superlattice mini-band, where Umklapp scattering becomes dominant. We also observe a T-linear conductance at these commensurate fillings over a range of temperatures. Strikingly, the T-linear conductance leads to a strongly suppressed Luttinger parameter, suggesting a state of extreme correlation.

cond-mat.str-el↗

arXiv2025

Monte Carlo Study of Critical Fermi Surface with Spatially Disordered Interactions

Non-Fermi liquids are an important topic in condensed matter physics, as their characteristics challenge the framework of traditional Fermi liquid theory and reveal the complex behavior of electrons in strongly interacting systems. Both the experimentally observed smeared region and the theoretically predicted marginal Fermi liquid suggest that spatial disorder seems to be an important driver of these phenomena. By performing large-scale determinant quantum Monte Carlo (DQMC) simulations in the ferromagnetic spin-fermion model at finite $N$, beyond the large-$N$ used in previous theoretical work, we investigated the role of spatial disorder in the critical Fermi surface (FS) of this model. We proposed a corrected theory of our system, which is based on a modified Eliashberg theory and a universal theory of strange metals. This theory agrees well with the data obtained from DQMC, particularly in capturing the $ω\ln ω$ type self-energy characteristic of marginal Fermi liquid behavior, and observing the linear-in-temperature resistivity. Our findings offer strong and unbiased validation of the universal theory of strange metals, broaden the applicability of the modified Eliashberg theory, and provide insights for numerically searching for marginal Fermi liquid and linear-in-temperature resistivity.

cond-mat.str-el↗

arXiv2025

Fermionic Partial Transpose in the Overlap Matrix Framework for Entanglement Negativity

Over the past two decades, the overlap matrix approach has been developed to compute quantum entanglement in free-fermion systems, particularly to calculate entanglement entropy and entanglement negativity. This method involves the use of partial trace and partial transpose operations within the overlap matrix framework. However, in previous studies, only the conventional partial transpose in fermionic systems has been considered, which does not account for fermionic anticommutation relations. Although the concept of a fermionic partial transpose was introduced by Shapourian et al. [Phys. Rev. B 95, 165101 (2017)], it has not yet been systematically incorporated into the overlap matrix framework. In this paper, we introduce the fermionic partial transpose into the overlap matrix approach, provide a systematic analysis of the validity of partial trace and partial transpose operations, and derive an explicit formula for calculating entanglement negativity in bipartite systems. Additionally, we numerically compute the logarithmic negativity of two lattice models to verify the Gioev-Klich-Widom scaling law. For tripartite geometries, we uncover limitations of the overlap matrix method and demonstrate that the previously reported logarithmic negativity result for a homogeneous one-dimensional chain in a disjoint interval geometry exceeds its theoretical upper bound.

quant-ph↗

arXiv2025

Untwisted and Twisted Rényi Negativities: Toward a Rényi Proxy for Logarithmic Negativity in Fermionic Systems

Entanglement entropy is a fundamental measure of quantum entanglement for pure states, but for large-scale many-body systems, Rényi entanglement entropy is much more computationally accessible. For mixed states, logarithmic negativity (LN) serves as a widely used entanglement measure, but its direct computation is often intractable, leaving Rényi negativity (RN) as the practical alternative. In fermionic systems, RN is further classified into untwisted and twisted types, depending on the definition of the fermionic partial transpose. However, which of these serves as the true Rényi proxy for LN has remained unclear -- until now. In this work, we address this question by developing a robust quantum Monte Carlo (QMC) method to compute both untwisted and twisted RNs, focusing on the rank-4 twisted RN, where non-trivial behavior emerges. We identify and overcome two major challenges: the singularity of the Green's function matrix and the exponentially large variance of RN estimators. Our method is demonstrated in the Hubbard model and the spinless $t$-$V$ model, revealing critical distinctions between untwisted and twisted RNs, as well as between rank-2 and high-rank RNs. Remarkably, we find that the twisted Rényi negativity ratio (RNR) adheres to the area law and decreases monotonically with temperature, in contrast to the untwisted RNR but consistent with prior studies of bosonic systems. This study not only establishes the twisted RNR as a more pertinent Rényi proxy for LN in fermionic systems but also provides comprehensive technical details for the stable and efficient computation of high-rank RNs. Our work lays the foundation for future studies of mixed-state entanglement in large-scale fermionic many-body systems.

cond-mat.str-el↗

arXiv2025

Delay Update in determinant quantum Monte Carlo

Determinant quantum Monte Carlo (DQMC) is a widely used unbiased numerical method for simulating strongly correlated electron systems. However, the update process in DQMC is often a bottleneck for its efficiency. To address this issue, we propose a generalized delay update scheme that can handle both onsite and extended interactions. Our delay update scheme can be implemented in both zero-temperature and finite-temperature versions of DQMC. We apply the delay update scheme to various strongly correlated electron models and evaluate its efficiency under different conditions. Our results demonstrate that the proposed delay update scheme significantly improves the efficiency of DQMC simulations, enable it to simulate larger system size.

cond-mat.str-el↗

arXiv2025

Spectroscopic evidence for possible quantum spin liquid behavior in a two-dimensional Mott insulator

Mott insulators with localized magnetic moments will exhibit a quantum spin liquid (QSL) state when the quantum fluctuations are strong enough to suppress the ordering of the spins. Such an entangled state will give rise to collective excitations, in which spin and charge information are carried separately. Our angle-resolved photoemission spectroscopy (ARPES) measurements on single-layer 1T-TaS2 show a flat band around the zone center and a gap opening of about 200 meV in the low temperature, indicating 2D Mott insulating nature in the system. This flat band is dispersionless in momentum space but shows anomalously broad width around the zone center and the spectral weight decays rapidly as momentum increases. The observation is described as a spectral continuum from electron fractionalization, corroborated by a low energy effective model.The intensity of the flat band is reduced by surface doping with magnetic adatoms and the gap is closing, a result from the interaction between spin impurities coupled with spinons and the chargons, which gives rise to a charge redistribution. Doping with nonmagnetic impurities behaves differently as the chemical potential shift dominates. These findings provide insight into the QSL states of strongly correlated electrons on 2D triangular lattices.

cond-mat.str-el↗

arXiv2025

Entanglement Rényi Negativity of Interacting Fermions from Quantum Monte Carlo Simulations

Many-body entanglement unveils additional aspects of quantum matter and offers insights into strongly correlated physics. While ground-state entanglement has received much attention in the past decade, the study of mixed-state quantum entanglement using negativity in interacting fermionic systems remains largely unexplored. We demonstrate that the partially transposed density matrix of interacting fermions, similar to their reduced density matrix, can be expressed as a weighted sum of Gaussian states describing free fermions, enabling the calculation of rank-$n$ Rényi negativity within the determinant quantum Monte Carlo framework. We calculate the rank-two Rényi negativity for the half-filled Hubbard model and the spinless $t$-$V$ model. Our calculation reveals that the area law coefficient of the Rényi negativity for the spinless $t$-$V$ model has a logarithmic finite-size scaling at the finite-temperature transition point. Our work contributes to the calculation of entanglement and sets the stage for future studies on quantum entanglement in various fermionic many-body mixed states.

cond-mat.str-el↗

arXiv2025

Residual entropy from temperature incremental Monte Carlo method

Residual entropy, which reflects the degrees of freedom in a system at absolute zero temperature, is crucial for understanding quantum and classical ground states. Despite its key role in explaining low-temperature phenomena and ground state degeneracy, accurately measuring residual entropy remains a difficult task owing to computational limitations. In this Letter, we introduce the temperature incremental Monte Carlo (TIMC) method, our approach to overcoming these challenges. The TIMC method incrementally calculates the partition function ratio of neighboring temperatures within Monte Carlo simulations, enabling precise entropy calculations and revealing other temperature-dependent properties in a single computational sweep of temperatures. We have rogorously tested TIMC on several complex systems, including the frustrated antiferromagnetic Ising model on both C60 and 2D triangular lattices, the Newman-Moore glassy model, and a 2D quantum transverse field Ising model. Notably, our method overcomes the difficulties encountered in partition function measurements when mapping $d$-dimensional quantum models to $d+1$-dimensional classical counterparts. These challenges arise from singular interactions that emerge in the small $Δ_τ$ limit during the quantum-to-classical mapping procedure. The TIMC method enables precise entropy calculations across the entire temperature range, as demonstrated in our studies of frustrated spin models, glassy phases, and phases exhibiting spontaneous symmetry breaking. This method's capability to calculate residual entropy could provide insights when applied to systems lacking analytical solutions.

cond-mat.stat-mech↗

arXiv2025

Boosting Determinant Quantum Monte Carlo with Submatrix Updates: Unveiling the Phase Diagram of the 3D Hubbard Model

Determinant Quantum Monte Carlo (DQMC) provides numerically exact solutions for strongly correlated fermionic systems but faces significant computational challenges with increasing system size. While submatrix updates were originally developed for Hirsch-Fye QMC with onsite interactions at finite temperatures [Phys. Rev. B 80, 195111 (2009)], their comprehensive application in DQMC has remained unexplored despite noted algorithmic similarities. We present the first comprehensive application of submatrix updates in DQMC, significantly extending beyond the original scope by enabling simulations with extended interactions and at zero temperature. Building upon conventional fast updates and delay updates, our generalized implementation achieves an order-of-magnitude improvement in computational efficiency, enabling simulations of the half-filled Hubbard model on lattices up to 8,000 sites - a scale previously challenging with standard DQMC implementations. This enhanced computational capability allows us to accurately determine the finite-temperature phase diagram of the 3D Hubbard model at half-filling. Our findings not only shed light on the phase transitions within these complex systems but also pave the way for more effective simulations of strongly correlated electrons, potentially guiding experimental efforts in cold atom simulations of the 3D Hubbard model.

cond-mat.str-el↗

arXiv2024

Fermionic skyrmions and bosonization for a Gross-Neveu transition

We investigate a 2+1-D interacting Dirac semimetal with onsite flavor SU(2) symmetry. Topological considerations imply that the skyrmions in the flavor-symmetry-breaking phase carry electron quantum numbers, motivating a dual bosonized low energy description in terms of two complex scalars coupled to an abelian Chern-Simons field. We propose that the transition between a nearby Chern insulator and the flavor symmetry-broken phase is a bicritical point in the bosonized description, and also suggest that the Gross-Neveu-Heisenberg (GNH) transition between the Dirac semimetal and the flavor symmetry-broken phase is a tricritical point. Heuristically, the dual description corresponds to the gap closing of fermionic skyrmions. We discuss implications and potential issues with our proposal, and motivated from it, perform extensive unbiased Determinantal Quantum Monte Carlo (DQMC) simulations on a lattice regularized Hamiltonian for the GNH transition, extending previously available results. We compare DQMC results with the estimates in the proposed dual from available perturbative renormalization group results. We also numerically demonstrate the presence of fermionic skyrmions in the symmetry-broken phase of our lattice model.

cond-mat.str-el↗

arXiv2023

Caution on Gross-Neveu criticality with a single Dirac cone: Violation of locality and its consequence of unexpected finite-temperature transition

Lately there are many SLAC fermion investigations on the (2+1)D Gross-Neveu criticality of a single Dirac cone [1,2]. While the SLAC fermion construction indeed gives rise to the linear energy-momentum relation for all lattice momenta at the non-interacting limit, the long-range hopping and its consequent violation of locality on the Gross-Neveu quantum critical point (GN-QCP) -- which a priori requires short-range interaction -- has not been verified. Here we show, by means of large-scale quantum Monte Carlo simulations, that the interaction-driven antiferromagnetic insulator in this case is fundamentally different from that on a purely local $π$-flux Hubbard model on the square lattice. In particular, we find the antiferromagnetic long-range order in the SLAC fermion model has a finite temperature continuous phase transition, which violates the Mermin-Wagner theorem, and smoothly connects to the previously determined GN-QCP. The magnetic excitations inside the antiferromagnetic insulator are gapped without Goldstone mode, even though the state spontaneously breaks continuous $SU(2)$ symmetry. These unusual results proclaim caution on the interpretation of the quantum phase transition in SLAC fermion model as that of GN-QCP with short-range interaction.

cond-mat.str-el↗

arXiv2022

Dirac fermions with plaquette interactions. III. SU(N) phase diagram with Gross-Neveu criticality and first-order phase transition

Inspired by our recent works[1, 2] of SU(2) and SU(4) Dirac fermions subjected to plaquette interactions on square lattice, here we extend the large-scale quantum Monte Carlo investigations to the phase digram of correlated Dirac fermions with SU(6) and SU(8) symmetries subjected to the plaquette interaction on the same lattice. From SU(2) to SU(8), the rich phase diagram exhibits a plethora of emerging quantum phases such as the Dirac semimetal, the antiferromagnetic Mott insulator, valence bond solid (VBS) and the Dirac spin liquid and phase transitions including the Gross-Neveu chiral transitions with emergent continuous symmetry, the deconfined quantum criticality and the first order transition between interaction-driven columnar VBS and plaquette VBS. These rich phenomena coming from the simple-looking lattice models, firmly convey the message that the interplay between the $SU(N)$ Dirac fermions -- with enhanced internal symmetries -- and extended plaquette interactions -- beyond the on-site Hubbard type -- is the new playground to synthesise novel highly entangled quantum matter both at the model level and with experimental feasibilities.

cond-mat.str-el↗