arXiv subjects

Xiao Yan Xu

Publications and source records attributed to Xiao Yan Xu.

At least 37 records · Page 2Linked to original sources

arXiv2022

Dirac fermions with plaquette interactions. II. SU(4) phase diagram with Gross-Neveu criticality and quantum spin liquid

At sufficiently low temperatures, interacting electron systems tend to develop orders. Exceptions are quantum critical point (QCP) and quantum spin liquid (QSL), where fluctuations prevent the highly entangled quantum matter to an ordered state down to the lowest temperature. While the ramification of these states may have appeared in high-temperature superconductors, ultra-cold atoms, frustrated magnets and quantum Moiré materials, their unbiased presence remain elusive in microscopic two-dimensional lattice models. Here, we show by means of large-scale quantum Monte Carlo simulations of correlated electrons on the $π$-flux square lattice subjected to extended Hubbard interaction, that a Gross-Neveu QCP separating massless Dirac fermions and an columnar valence bond solid at finite interaction, and a possible Dirac QSL at the infinite yet tractable interaction limit emerge in a coherent sequence. These unexpected novel quantum states resides in this simple-looking model, unifying ingredients including emergent symmetry, deconfined fractionalization and the dynamic coupling between emergent matter and gauge fields, will have profound implications both in quantum many-body theory and understanding of the aforementioned experimental systems.

cond-mat.str-el↗

arXiv2022

Dirac fermions with plaquette interactions. I. SU(2) phase diagram with Gross-Neveu and deconfined quantum criticalities

We investigate the ground state phase diagram of an extended Hubbard model with $π$-flux hopping term at half-filling on a square lattice, with unbiased large-scale auxiliary-field quantum Monte Carlo simulations. As a function of interaction strength, there emerges an intermediate phase which realizes two interaction-driven quantum critical points, with the first between the Dirac semimetal and an insulating phase of weak valence bond solid (VBS) order, and the second separating the VBS order and an antiferromagnetic insulating phase. These intriguing quantum critical points are respectively bestowed with Gross-Neveu and deconfined quantum criticalities, and the critical exponents $η_\text{VBS}=0.6(1)$ and $η_\text{AF}=0.58(3)$ at deconfined quantum critical point satisfy the CFT Bootstrap bound. We also investigate the dynamical properties of the spin excitation and find the spin gap open near the first transition and close at the second. The relevance of our findings in realizing deconfined quantum criticality in fermion systems and the implication to lattice models with further extended interactions such as those in quantum Moiré systems, are discussed.

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arXiv2022

Fermion sign bounds theory in quantum Monte Carlo simulation

Sign problem in fermion quantum Monte Carlo (QMC) simulation appears to be an extremely hard problem. Traditional lore passing around for years tells people that when there is a sign problem, the average sign in QMC simulation approaches zero exponentially fast with the space-time volume of the configurational space. We, however, analytically show this is not always the case and manage to find physical bounds for the average sign. Our understanding is based on a direct connection between the sign bounds and a well-defined partition function of reference system and could distinguish when the bounds have the usual exponential scaling, and when they are bestowed on an algebraic scaling at low temperature limit. We analytically explain such algebraic sign problems found in flat band moiré lattice models at low temperature limit. At finite temperature, a domain size argument based on sign bounds also explains the connection between sign behavior and finite temperature phase transition. Sign bounds, as a well-defined observable, may have ability to ease or even make use of the sign problem.

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arXiv2021

Projection of Infinite-$U$ Hubbard Model and Algebraic Sign Structure

We propose a projection approach to perform quantum Monte Carlo (QMC) simulation on the infinite-$U$ Hubbard model at some integer fillings where either it is sign problem free or surprisingly has an algebraic sign structure -- a power law dependence of average sign on system size. We demonstrate our scheme on the infinite-$U$ $SU(2N)$ fermionic Hubbard model on both a square and honeycomb lattice at half-filling, where it is sign problem free, and suggest possible correlated ground states. The method can be generalized to study certain extended Hubbard models applying to cluster Mott insulators or two-dimensional Moiré systems; among one of them at certain non-half-integer filling, the sign has an algebraic behavior such that it can be numerically solved within a polynomial time. Further, our projection scheme can also be generalized to implement the Gutzwiller projection to spin basis such that $SU(2N)$ quantum spin models and Kondo lattice models may be studied in the framework of fermionic QMC simulations.

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arXiv2021

Topological Superconductivity in Multifold Fermion Metals

Recently, multifold fermions characterized by band crossings with multifold degeneracy and Fermi surfaces with nontrivial Chern numbers have been discovered experimentally in AlPt[arXiv:1812.03310] and XSi(X=Rh,Co)[arXiv:1812.04466][arXiv:1901.03358][arXiv:1809.01312]. In this work, we largely expand the family of multifold fermion materials by pointing out that several well-studied noncentrosymmetric superconductors are indeed multifold fermion metals. Importantly, their normal state topological properties, which have been ignored in previous studies, play an important role in the superconducting properties. Taking Li$_2$Pd$_3$B and Li$_2$Pt$_3$B as examples, we found a large number of unconventional degenerate points, such as double spin-1, spin-3/2, Weyl and double Weyl topological band crossing points near the Fermi energy, which result in finite Chern numbers on Fermi surfaces. Long Fermi arc states in Li$_2$Pd$_3$B, originating from the nontrivial band topology were found. Importantly, it has been shown experimentally that Li$_2$Pd$_3$B and Li$_2$Pt$_3$B are fully gapped and gapless superconductors, respectively. By analyzing the possible pairing symmetries, we suggest that Li$_2$Pd$_3$B can be a DIII class topological superconductor with Majorana surface states, even though the spin-orbit coupling in Li$_2$Pd$_3$B is negligible. Interestingly, Li$_2$Pt$_3$B, being gapless, is likely to be a nodal topological superconductor with dispersionless surface Majorana modes. We further identified that several noncentrosymmetric superconductors, such as Mo$_3$Al$_2$C, PdBiSe, Y$_2$C$_3$ and La$_2$C$_3$, are multifold fermion superconductors whose normal state topological properties have been ignored in previous experimental and theoretical studies.

cond-mat.supr-con↗

arXiv2021

Competing nodal d-wave superconductivity and antiferromagnetism

Competing unconventional superconductivity and antiferromagnetism widely exist in several strongly correlated quantum materials whose direct simulation generally suffers from fermion sign problem. Here we report unbiased Quantum Monte Carlo (QMC) simulations on a sign-problem-free repulsive toy model with same onsite symmetries as the standard Hubbard model on a 2D square lattice. Using QMC, supplemented with mean-field and continuum field-theory arguments, we find that it hosts three distinct phases: a nodal d-wave phase, an antiferromagnet, and an intervening phase which hosts coexisting antiferromagnetism and nodeless d-wave superconductivity. The transition from the coexisting phase to the antiferromagnet is described by the 2+1-D XY universality class, while the one from the coexisting phase to the nodal d-wave phase is described by the Heisenberg-Gross-Neveu theory. The topology of our phase diagram resembles that of layered organic materials which host pressure tuned Mott transition from antiferromagnet to unconventional superconductor at half-filling.

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arXiv2021

Kramers Nodal Line Metals

Recently, it was pointed out that all chiral crystals with spin-orbit coupling (SOC) can be Kramers Weyl semimetals (KWSs) which possess Weyl points pinned at time-reversal invariant momenta. In this work, we show that all achiral non-centrosymmetric materials with SOC can be a new class of topological materials, which we term Kramers nodal line metals (KNLMs). In KNLMs, there are doubly degenerate lines, which we call Kramers nodal lines (KNLs), connecting time-reversal invariant momenta. The KNLs create two types of Fermi surfaces, namely, the spindle torus type and the octdong type. Interestingly, all the electrons on octdong Fermi surfaces are described by two-dimensional massless Dirac Hamiltonians. These materials support quantized optical conductance in thin films. We further show that KNLMs can be regarded as parent states of KWSs. Therefore, we conclude that all non-centrosymmetric metals with SOC are topological, as they can be either KWSs or KNLMs.

cond-mat.mes-hall↗

arXiv2021

Kramers Weyl Semimetals as Quantum Solenoids and Their Applications in Spin-Orbit Torque Devices

Kramers Weyl semimetals are Weyl semimetals that have Weyl points pinned at the time reversal invariant momenta. Recently it has been discovered that all chiral crystals host Weyl points at time reversal invariant momenta, so metals with chiral lattice symmetry all belong to the category of Kramers Weyl semimetals. In this work, we show that due to the chiral lattice symmetry, Kramers Weyl semimetals have the unique longitudinal magnetoelectric effect in which the charge current induced spin and orbital magnetization is parallel to the direction of the current. This feature allows Kramers Weyl semimetals to act as nanoscale quantum solenoids with both orbital and spin magnetization. As the moving electrons of Kramers Weyl semimetal can generate longitudinal magnetization, Kramers Weyl semimetals can be used for new designs of spin-orbit torque devices with all electric control of magnetization switching for magnets with perpendicular magnetic anisotropy.

cond-mat.mes-hall↗

arXiv2021

Correlation-induced insulating topological phases at charge neutrality in twisted bilayer graphene

Twisted bilayer graphene (TBG) provides a unique framework to elucidate the interplay between strong correlations and topological phenomena in two-dimensional systems. The existence of multiple electronic degrees of freedom -- charge, spin, and valley -- gives rise to a plethora of possible ordered states and instabilities. Identifying which of them are realized in the regime of strong correlations is fundamental to shed light on the nature of the superconducting and correlated insulating states observed in the TBG experiments. Here, we use unbiased, sign-problem-free quantum Monte Carlo simulations to solve an effective interacting lattice model for TBG at charge neutrality. Besides the usual cluster Hubbard-like repulsion, this model also contains an assisted hopping interaction that emerges due to the non-trivial topological properties of TBG. Such a non-local interaction fundamentally alters the phase diagram at charge neutrality, gapping the Dirac cones even for infinitesimally small interaction. As the interaction strength increases, a sequence of different correlated insulating phases emerge, including a quantum valley Hall state with topological edge states, an intervalley-coherent insulator, and a valence bond solid. The charge-neutrality correlated insulating phases discovered here provide the sought-after reference states needed for a comprehensive understanding of the insulating states at integer fillings and the proximate superconducting states of TBG.

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arXiv2021

Correlated Insulating Phases in the Twisted Bilayer Graphene

We review analytical and numerical studies of correlated insulating states in twisted bilayer graphene, focusing on real-space lattice models constructions and their unbiased quantum many-body solutions. We show that by constructing localized Wannier states for the narrow bands, the projected Coulomb interactions can be approximated by interactions of cluster charges with assisted nearest neighbor hopping terms. With the interaction part only, the Hamiltonian is $SU(4)$ symmetric considering both spin and valley degrees of freedom. In the strong coupling limit where the kinetic terms are neglected, the ground states are found to be in the $SU(4)$ manifold with degeneracy. The kinetic terms, treated as perturbation, break this large $SU(4)$ symmetry and propel the appearance of intervalley coherent state, quantum topological insulators and other symmetry-breaking insulating states. We first present the theoretical analysis of moiré lattice model construction and then show how to solve the model with large-scale quantum Monte Carlo simulations in an unbiased manner. We further provide potential directions such that from the real-space model construction and its quantum many-body solutions how the perplexing yet exciting experimental discoveries in the correlation physics of twisted bilayer graphene can be gradually understood. This review will be helpful for the readers to grasp the fast growing field of the model study of twisted bilayer graphene.

cond-mat.str-el↗

arXiv2020

Identification of non-Fermi liquid fermionic self-energy from quantum Monte Carlo data

Quantum Monte Carlo (QMC) simulations of correlated electron systems provide unbiased information about system behavior at a quantum critical point (QCP) and can verify or disprove the existing theories of non-Fermi liquid (NFL) behavior at a QCP. However, simulations are carried out at a finite temperature, where quantum-critical features are masked by finite temperature effects. Here we present a theoretical framework within which it is possible to separate thermal and quantum effects and extract the information about NFL physics at $T=0$. We demonstrate our method for a specific example of 2D fermions near a Ising-ferromagnetic QCP. We show that one can extract from QMC data the zero-temperature form of fermionic self-energy $Σ(ω)$ even though the leading contribution to the self-energy comes from thermal effects. We find that the frequency dependence of $Σ(ω)$ agrees well with the analytic form obtained within the Eliashberg theory of dynamical quantum criticality, and obeys $ω^{2/3}$ scaling at low frequencies. Our results open up an avenue for QMC studies of quantum-critical metals.

cond-mat.str-el↗

arXiv2020

Confinement transition in the QED$_3$-Gross-Neveu-XY universality class

The coupling between fermionic matter and gauge fields plays a fundamental role in our understanding of nature, while at the same time posing a challenging problem for theoretical modeling. In this situation, controlled information can be gained by combining different complementary approaches. Here, we study a confinement transition in a system of $N_f$ flavors of interacting Dirac fermions charged under a U(1) gauge field in 2+1 dimensions. Using Quantum Monte Carlo simulations, we investigate a lattice model that exhibits a continuous transition at zero temperature between a gapless deconfined phase, described by three-dimensional quantum electrodynamics, and a gapped confined phase, in which the system develops valence-bond-solid order. We argue that the quantum critical point is in the universality class of the QED$_3$-Gross-Neveu-XY model. We study this field theory within a $1/N_f$ expansion in fixed dimension as well as a renormalization group analysis in $4-ε$ space-time dimensions. The consistency between numerical and analytical results is revealed from large to intermediate flavor number.

cond-mat.str-el↗

arXiv2020

Metal to Orthogonal Metal Transition

Orthogonal metal is a new quantum metallic state that conducts electricity but acquires no Fermi surface (FS) or quasiparticles, and hence orthogonal to the established paradigm of Landau's Fermi-liquid (FL). Such a state may hold the key of understanding the perplexing experimental observations of quantum metals that are beyond FL, i.e., dubbed non-Fermi-liquid (nFL), ranging from the Cu- and Fe-based oxides, heavy fermion compounds to the recently discovered twisted graphene heterostructures. However, to fully understand such an exotic state of matter, at least theoretically, one would like to construct a lattice model and to solve it with unbiased quantum many-body machinery. Here we achieve this goal by designing a 2D lattice model comprised of fermionic and bosonic matter fields coupled with dynamic $\mathbb Z_2$ gauge fields, and obtain its exact properties with sign-free quantum Monte Carlo simulations. We find that as the bosonic matter fields become disordered, with the help of deconfinement of the $\mathbb Z_2$ gauge fields, the system reacts with changing its nature from the conventional normal metal with an FS to an orthogonal metal of nFL without FS and quasiparticles and yet still responds to magnetic probe like an FL. Such a quantum phase transition from a normal metal to an orthogonal metal, with its electronic and magnetic spectral properties revealed, is calling for the establishment of new paradigm of quantum metals and their transition with conventional ones.

cond-mat.str-el↗

arXiv2019

Is magic-angle twisted bilayer graphene near a quantum critical point?

An extended Hubbard model on a honeycomb lattice with two orbitals per site at charge neutrality is investigated with unbiased large-scale quantum Monte Carlo simulations. The Fermi velocity of the Dirac fermions is renormalized as the cluster charge interaction increases, until a mass term emerges and a quantum phase transition from Dirac semi-metal to valence bond solid (VBS) insulator is established. The quantum critical point is discovered to belong to 3D $N=4$ Gross-Neveu chiral XY universality with the critical exponents obtained at high precision. Further enhancement of the interaction drives the system into two different VBS phases, the properties and transition between them are also revealed. Since the model is related to magic-angle twisted bilayer graphene, our results may have relevance towards the symmetry breaking order at the charge neutrality point of the material, and associate the wide range of universal strange metal behavior around it with quantum critical fluctuations.

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arXiv2019

Revealing Fermionic Quantum Criticality from New Monte Carlo Techniques

This review summarizes recent developments in the study of fermionic quantum criticality, focusing on new progress in numerical methodologies, especially quantum Monte Carlo methods, and insights that emerged from recently large-scale numerical simulations. Quantum critical phenomena in fermionic systems have attracted decades of extensive research efforts, partially lured by their exotic properties and potential technology applications and partially awaked by the profound and universal fundamental principles that govern these quantum critical systems. Due to the complex and non-perturbative nature, these systems belong to the most difficult and challenging problems in the study of modern condensed matter physics, and many important fundamental problems remain open. Recently, new developments in model design and algorithm improvements enabled unbiased large-scale numerical solutions to be achieved in the close vicinity of these quantum critical points, which paves a new pathway towards achieving controlled conclusions through combined efforts of theoretical and numerical studies, as well as possible theoretical guidance for experiments in heavy-fermion compounds, Cu-based and Fe-based superconductors, ultra-cold fermionic atomic gas, twisted graphene layers, etc., where signatures of fermionic quantum criticality exist.

cond-mat.str-el↗

arXiv2019

Dynamics of Compact Quantum Electrodynamics at Large Fermion Flavor

Thanks to the development in quantum Monte Carlo technique, the compact U(1) lattice gauge theory coupled to fermionic matter at (2+1)D is now accessible with large-scale numerical simulations, and the ground state phase diagram as a function of fermion flavor ($N_f$) and the strength of gauge fluctuations is mapped out~\cite{Xiao2018Monte}. Here we focus on the large fermion flavor case ($N_f=8$) to investigate the dynamic properties across the deconfinement-to-confinement phase transition. In the deconfined phase, fermions coupled to the fluctuating gauge field to form U(1) spin liquid with continua in both spin and dimer spectral functions, and in the confined phase fermions are gapped out into valence bond solid phase with translational symmetry breaking and gapped spectra. The dynamical behaviors provide supporting evidence for the existence of the U(1) deconfined phase and could shine light on the nature of the U(1)-to-VBS phase transition which is of the QED$_3$-Gross-Neveu chiral O(2) universality whose properties still largely unknown.

cond-mat.str-el↗

arXiv2019

Itinerant Quantum Critical Point with Fermion Pockets and Hot Spots

Metallic quantum criticality is among the central theme in the understanding of correlated electronic systems, and converging results between analytical and numerical approaches are still under calling. In this work, we develop state-of-art large scale quantum Monte Carlo simulation technique and systematically investigate the itinerant quantum critical point on a 2D square lattice with antiferromagnetic spin fluctuations at wavevector $\mathbf{Q}=(π,π)$ -- a problem that resembles the Fermi surface setup and low-energy antiferromagnetic fluctuations in high-Tc cuprates and other critical metals, which might be relevant to their non-Fermi-liquid behaviors. System sizes of $60\times 60 \times 320$ ($L \times L \times L_τ$) are comfortably accessed, and the quantum critical scaling behaviors are revealed with unprecedingly high precision. We found that the antiferromagnetic spin fluctuations introduce effective interactions among fermions and the fermions in return render the bare bosonic critical point into a new universality, different from both the bare Ising universality class and the Hertz-Mills-Moriya RPA prediction. At the quantum critical point, a finite anomalous dimension $η\sim 0.125$ is observed in the bosonic propagator, and fermions at hot spots evolve into a non-Fermi-liquid. In the antiferromagnetically ordered metallic phase, fermion pockets are observed as energy gap opens up at the hot spots. These results bridge the recent theoretical and numerical developments in metallic quantum criticality and can be served as the stepping stone towards final understanding of the 2D correlated fermions interacting with gapless critical excitations.

cond-mat.str-el↗

arXiv2019

Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: the Parent State of Quantum Phases

The interplay between lattice gauge theories and fermionic matter accounts for fundamental physical phenomena ranging from the deconfinement of quarks in particle physics to quantum spin liquid with fractionalized anyons and emergent gauge structures in condensed matter physics. However, except for certain limits (for instance large number of flavors of matter fields), analytical methods can provide few concrete results. Here we show that the problem of compact $U(1)$ lattice gauge theory coupled to fermionic matter in $(2+1)$D is possible to access via sign-problem-free quantum Monte Carlo simulations. One can hence map out the phase diagram as a function of fermion flavors and the strength of gauge fluctuations. By increasing the coupling constant of the gauge field, gauge confinement in the form of various spontaneous symmetry breaking phases such as valence bond solid (VBS) and Néel antiferromagnet emerge. Deconfined phases with algebraic spin and VBS correlation functions are also observed. Such deconfined phases are an incarnation of exotic states of matter, $i.e.$ the algebraic spin liquid, which is generally viewed as the parent state of various quantum phases. The phase transitions between deconfined and confined phases, as well as that between the different confined phases provide various manifestations of deconfined quantum criticality. In particular, for four flavors, $N_f = 4$, our data suggests a continuous quantum phase transition between the VBS and Néel order. We also provide preliminary theoretical analysis for these quantum phase transitions.

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