arXiv subjects

Zi Hong Liu

Publications and source records attributed to Zi Hong Liu.

13 recordsLinked to original sources

arXiv2026

Interaction-induced nematic Dirac semimetal from quadratic band touching: A constrained-path quantum Monte Carlo study

Electronic systems with quadratic band touchings, commonly found in two- and three-dimensional materials such as Bernal-stacked bilayer graphene, kagome metals, HgTe, and pyrochlore iridates, have attracted significant interest concerning the role of interactions in shaping their electronic properties. However, even in the simplest model of spinless fermions on a two-dimensional checkerboard lattice, the quantum phase diagram as a function of nearest-neighbor interaction remains under debate. We employ constrained-path quantum Monte Carlo simulations (CP-QMC) simulations to investigate the problem using a two-dimensional torus geometry. We cross-validate our results on small lattices by comparing them with density-matrix renormalization group calculations, finding quantitative agreement. In particular, we implement an improved optimization scheme within the CP-QMC simulations, enabling the identification of a bond-nematic Dirac semimetal phase that was found in tensor-network studies on cylindrical geometries, but remains inaccessible to Hartree-Fock mean-field methods. The CP-QMC approach makes it possible to establish the emergence of this phase in a geometry that preserves lattice rotational symmetry and permits extrapolation to the thermodynamic limit. Our results show that the quantum phase diagram of spinless fermions on the checkerboard lattice with nearest-neighbor repulsion features three interaction-induced phases at half filling: a quantum anomalous Hall insulator at weak coupling, a bond-nematic Dirac semimetal at intermediate coupling, and a site-nematic insulator at strong coupling.

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arXiv2026

Emergent relativistic symmetry from interacting fermions on the honeycomb bilayer

We study the phase diagram of interacting spinless fermions on the honeycomb bilayer at charge neutrality using large-scale quantum Monte Carlo simulations. In the noninteracting limit, the low-energy spectrum features quadratically dispersing bands that touch at the corners of the hexagonal Brillouin zone. Weak to intermediate interactions induce a splitting of each of the quadratic band touching points into four Dirac points, located along high-symmetry directions of the reciprocal lattice. Strong interactions lead to the formation of a layer-polarized charge density wave, which spontaneously breaks the $\mathbb Z_2$ layer inversion symmetry and opens an insulating gap in the spectrum. We show that the semimetal-to-insulator quantum phase transition as a function of interaction is continuous and characterized by emergent relativistic symmetry. Our results for the values of the correlation-length exponent $ν$, the order-parameter anomalous dimension $η_ϕ$, and the fermion anomalous dimension $η_ψ$ agree with those of the theoretically predicted 2+1D Gross-Neveu-Ising universality class with eight two-component Dirac fermions within less than 5\%\ deviation. We also determine the crossover scale as a function of interaction strength between the nonrelativistic semimetal state at high temperatures, characterized by dynamical critical exponent $z = 2$, and the Dirac semimetal state at intermediates temperatures, characterized by $z=1$. Further reducing the temperature below the crossover scale at a fixed value of the interaction strength above the quantum critical point results in a classical ordering transition in the 2D Ising universality class.

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arXiv2024

Critical properties of metallic and deconfined quantum phase transitions in Dirac systems

We characterize, by means of large-scale fermion quantum Monte Carlo simulations, metallic and deconfined quantum phase transitions in a bilayer honeycomb model in terms of their quantum critical and finite-temperature properties.The model features three different phases at zero temperature as function of interaction strength. At weak interaction, a fully symmetric Dirac semimetal state is realized. At intermediate and strong interaction, respectively, two long-range-ordered phases that break different symmetries are stabilized. The ordered phases feature partial and full, respectively, gap openings in the fermion spectrum. The first transition between the disordered and long-range-ordered semimetallic phases has previously been argued to be described by the $(2+1)$-dimensional Gross-Neveu-SO(3) field theory. By performing simulations with an improved symmetric Trotter decomposition, we further substantiate this claim by computing the critical exponents $1/ν$, $η_ϕ$, and $η_ψ$, which turn out to be consistent with the field-theoretical expectation within numerical and analytical uncertainties. The second transition between the two long-range-ordered phases has previously been proposed as a possible instance of a metallic deconfined quantum critical point. We further develop this scenario by analyzing the spectral functions in the single-particle, particle-hole, and particle-particle channels. Our results indicate gapless excitations with a unique velocity, supporting the emergence of Lorentz symmetry at criticality. We also compute the finite-temperature phase boundaries of the ordered states above the fully gapped state at large interaction. The phase boundaries vanishes smoothly in the vicinity of the putative metallic deconfined quantum critical point, in agreement with the expectation for a continuous or weakly-first-order transition.

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arXiv2024

Disorder Operator and Rényi Entanglement Entropy of Symmetric Mass Generation

In recent years a consensus has gradually been reached that the previously proposed deconfined quantum critical point (DQCP) for spin-1/2 systems, an archetypal example of quantum phase transition beyond the classic Landau's paradigm, actually does not correspond to a true unitary conformal field theory (CFT). In this work we carefully investigate another type of quantum phase transition supposedly beyond the similar classic paradigm, the so called ``symmetric mass generation" (SMG) transition proposed in recent years. We employ the sharp diagnosis including the scaling of disorder operator and Rényi entanglement entropy in large-scale lattice model quantum Monte Carlo simulations. Our results strongly suggest that the SMG transition is indeed an unconventional quantum phase transition and it should correspond to a true $(2+1)d$ unitary CFT.

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arXiv2023

Fermion disorder operator at Gross-Neveu and deconfined quantum criticalities

The fermion disorder operator has been shown to reveal the entanglement information in 1D Luttinger liquids and 2D free and interacting Fermi and non-Fermi liquids emerging at quantum critical points(QCP). Here we study, by means of large-scale quantum Monte Carlo simulation, the scaling behavior of disorder operator in correlated Dirac systems. We first demonstrate the logarithmic scaling behavior of the disorder operator at the Gross-Neveu (GN) chiral Ising and Heisenberg QCPs, where consistent conformal field theory (CFT) content of the GN-QCP in its coefficient is found. Then we study a 2D monopole free deconfined quantum critical point (DQCP) realized between a quantum-spin Hall insulator and a superconductor. Our data point to negative values of the logarithmic coefficients such that the DQCP does not correspond to a unitary CFT. Density matrix renormalization group calculations of the disorder operator on a 1D DQCP model also detect emergent continuous symmetries.

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arXiv2023

Many versus one: the disorder operator and entanglement entropy in fermionic quantum matter

Motivated by recent development of the concept of the disorder operator and its relation with entanglement entropy in bosonic systems, here we show the disorder operator successfully probes many aspects of quantum entanglement in fermionic many-body systems. From both analytical and numerical computations in free and interacting fermion systems in 1D and 2D, we find the disorder operator and the entanglement entropy exhibit similar universal scaling behavior, as a function of the boundary length of the subsystem, but with subtle yet important differences. In 1D they both follow the $\log{L}$ scaling behavior with the coefficient determined by the Luttinger parameter for disorder operator, and the conformal central charge for entanglement entropy. In 2D they both show the universal $L\log L$ scaling behavior in free and interacting Fermi liquid states, with the coefficients depending on the geometry of the Fermi surfaces. However at a 2D quantum critical point with non-Fermi-liquid state, extra symmetry information is needed in the design of the disorder operator, so as to reveal the critical fluctuations as does the entanglement entropy. Our results demonstrate the fermion disorder operator can be used to probe quantum many-body entanglement related to global symmetry, and provides new tools to explore the still largely unknown territory of highly entangled fermion quantum matter in 2 or higher dimensions.

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arXiv2023

Magnetic quantum phase transition in a metallic Kondo heterostructure

We consider a two-dimensional quantum spin system described by a Heisenberg model that is embedded in a three-dimensional metal. The two systems couple via an antiferromagnetic Kondo interaction. In such a setup, the ground state generically remains metallic down to the lowest temperatures and allows us to study magnetic quantum phase transitions in metallic environments. From the symmetry point of view, translation symmetry is present in two out of three lattice directions such that crystal momentum is only partially conserved. Importantly, the construction provides a route to study, with negative-sign-free auxiliary-field quantum Monte Carlo methods, the physics of local moments in metallic environments. Our large-scale numerical simulations show that as a function of the Kondo coupling, the system has two metallic phases. In the limit of strong Kondo coupling, a paramagnetic heavy-fermion phase emerges. Here, the spin degree of freedom is screened by means of the formation of a composite quasiparticle that participates in the Luttinger count. At weak Kondo coupling, magnetic order is present. This phase is characterized by Landau-damped Goldstone modes. Furthermore, the aforementioned composite quasiparticle remains intact across the quantum phase transition.

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arXiv2022

Marginal Fermi liquid at magnetic quantum criticality from dimensional confinement

Metallic quantum criticality is frequently discussed as a source for non-Fermi liquid behavior, but controlled theoretical treatments are scarce. Here we identify and study a novel magnetic quantum critical point in a two-dimensional antiferromagnet coupled to a three-dimensional environment of conduction electrons. Using sign-problem-free quantum Monte Carlo simulations and an effective field-theory analysis, we demonstrate that the quantum critical point is characterized by marginal Fermi liquid behavior. In particular, we compute the electrical resistivity for transport across the magnetic layer, which is shown to display a linear temperature dependence at criticality. Experimental realizations in Kondo heterostructures are discussed.

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arXiv2022

Metallic and Deconfined Quantum Criticality in Dirac Systems

Motivated by the physics of spin-orbital liquids, we study a model of interacting Dirac fermions on a bilayer honeycomb lattice at half filling, featuring an explicit global SO(3)$\times$U(1) symmetry. Using large-scale auxiliary-field quantum Monte Carlo (QMC) simulations, we locate two zero-temperature phase transitions as function of increasing interaction strength. First, we observe a continuous transition from the weakly-interacting semimetal to a different semimetallic phase in which the SO(3) symmetry is spontaneously broken and where two out of three Dirac cones acquire a mass gap. The associated quantum critical point can be understood in terms of a Gross-Neveu-SO(3) theory. Second, we subsequently observe a transition towards an insulating phase in which the SO(3) symmetry is restored and the U(1) symmetry is spontaneously broken. While strongly first order at the mean-field level, the QMC data is consistent with a direct and continuous transition. It is thus a candidate for a new type of deconfined quantum critical point that features gapless fermionic degrees of freedom.

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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.

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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.

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arXiv2018

EMUS-QMC: Elective Momentum Ultra-Size Quantum Monte Carlo Method

One bottleneck of quantum Monte Carlo (QMC) simulation of strongly correlated electron systems lies at the scaling relation of computational complexity with respect to the system sizes. For generic lattice models of interacting fermions, the best methodology at hand still scales with $βN^3$ where $β$ is the inverse temperature and $N$ is the system size. Such scaling behavior has greatly hampered the accessibility of the universal infrared (IR) physics of many interesting correlated electron models at (2+1)D, let alone (3+1)D. To reduce the computational complexity, we develop a new QMC method with inhomogeneous momentum-space mesh, dubbed elective momentum ultra-size quantum Monte Carlo (EQMC) method. Instead of treating all fermionic excitations on an equal footing as in conventional QMC methods, by converting the fermion determinant into the momentum space, our method focuses on fermion modes that are directly associated with low-energy (IR) physics in the vicinity of the so-called hot-spots, while other fermion modes irrelevant for universal properties are ignored. As shown in the manuscript, for any cutoff-independent quantities, e.g. scaling exponents, this method can achieve the same level of accuracy with orders of magnitude increase in computational efficiency. We demonstrate this method with a model of antiferromagnetic itinerant quantum critical point, realized via coupling itinerant fermions with a frustrated transverse-field Ising model on a triangle lattice. The system size of $48 \times 48 \times 32$ ($L\times L\timesβ$, almost 3 times of previous investigations) are comfortably accessed with EQMC. With much larger system sizes, the scaling exponents are unveiled with unprecedentedly high accuracy, and this result sheds new light on the open debate about the nature and the universality class of itinerant quantum critical points.

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arXiv2018

Itinerant quantum critical point with frustration and non-Fermi-liquid

Employing the self-learning quantum Monte Carlo algorithm, we investigate the frustrated transverse-field triangle-lattice Ising model coupled to a Fermi surface. Without fermions, the spin degrees of freedom undergoes a second-order quantum phase transition between paramagnetic and clock-ordered phases. This quantum critical point (QCP) has an emergent U(1) symmetry and thus belongs to the (2+1)D XY universality class. In the presence of fermions, spin fluctuations introduce effective interactions among fermions and distort the bare Fermi surface towards an interacting one with hot spots and Fermi pockets. Near the QCP, non-Fermi-liquid behavior are observed at the hot spots, and the QCP is rendered into a different universality with Hertz-Millis type exponents. The detailed properties of this QCP and possibly related experimental systems are also discussed.

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