Zi Hong Liu
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Research Interests
Zi Hong Liu has a total of 19 co-authors. Here are the top co-authors by number of shared publications:
Fakher F. Assaad
Universität Würzburg
5 shared publications- Lukas Janssen
TU Dresden
5 shared publications Matthias Vojta
Institut für Theoretische Physik and Würzburg-Dresden Cluster of Excellence ct.qmat, Technische Universität Dresden, 01062 Dresden, Germany
3 shared publications- Bernhard Frank
Institut für Theoretische Physik and Würzburg-Dresden Cluster of Excellence ct.qmat, Technische Universität Dresden, 01062 Dresden, Germany
2 shared publications Weilun Jiang
State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China
2 shared publications- Zi Yang Meng
The University of Hong Kong
2 shared publications
Latest Publications
- 23 October 2026
- Published by American Physical Society (APS) in Physical Review B
- Vol. 114 (23) , L231111
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 $\ensuremath{\nu}$, the order-parameter anomalous dimension ${\ensuremath{\eta}}_{\ensuremath{\phi}}$, and the fermion anomalous dimension ${\ensuremath{\eta}}_{\ensuremath{\psi}}$ agree with those of the theoretically predicted (2+1)-dimension 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 two-dimensional Ising universality class.- 23 October 2026
- Published by American Physical Society (APS) in Physical Review B
- Vol. 114 (23) , L231111
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 $\ensuremath{\nu}$, the order-parameter anomalous dimension ${\ensuremath{\eta}}_{\ensuremath{\phi}}$, and the fermion anomalous dimension ${\ensuremath{\eta}}_{\ensuremath{\psi}}$ agree with those of the theoretically predicted (2+1)-dimension 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 two-dimensional Ising universality class.- 11 September 2024
- Published by American Physical Society (APS) in Physical Review B
- Vol. 110 (12) , 125123
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 distinct phases at zero temperature as a 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, each breaking different symmetries are stabilized. The ordered phases feature partial and full gap openings in the fermion spectrum, respectively. We clarify the symmetries of the different zero-temperature phases and the symmetry-breaking patterns across the two quantum phase transitions between them. The first transition between the disordered and long-range-ordered semimetallic phases has previously been argued to be described by the -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 , , and , 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 boundary 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.- 11 September 2024
- Published by American Physical Society (APS) in Physical Review B
- Vol. 110 (12) , 125123
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 distinct phases at zero temperature as a 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, each breaking different symmetries are stabilized. The ordered phases feature partial and full gap openings in the fermion spectrum, respectively. We clarify the symmetries of the different zero-temperature phases and the symmetry-breaking patterns across the two quantum phase transitions between them. The first transition between the disordered and long-range-ordered semimetallic phases has previously been argued to be described by the -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 , , and , 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 boundary 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.- 12 April 2024
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 132 (15)
Disorder Operator and Rényi Entanglement Entropy of Symmetric Mass Generation
- 12 April 2024
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 132 (15)
Disorder Operator and Rényi Entanglement Entropy of Symmetric Mass Generation
- 26 September 2023
- Published by American Physical Society (APS) in Physical Review B
- Vol. 108 (10) , L100405
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 effectively acts like a Kondo impurity. Due to the presence of the marginal Fermi liquid excitations, the resistivity exhibits a linear decrease with temperature at criticality, in contrast to the usual quadratic decrease. Experimental realizations in Kondo heterostructures are discussed.
- 26 September 2023
- Published by American Physical Society (APS) in Physical Review B
- Vol. 108 (10) , L100405
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 effectively acts like a Kondo impurity. Due to the presence of the marginal Fermi liquid excitations, the resistivity exhibits a linear decrease with temperature at criticality, in contrast to the usual quadratic decrease. Experimental realizations in Kondo heterostructures are discussed.
- Top Cited Papers
- 28 June 2023
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 130 (26) , 266501
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 (QCPs) [W. Jiang et al., arXiv:2209.07103]. Here we study, by means of large-scale quantum Monte Carlo simulation, the scaling behavior of the 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.
- 28 June 2023
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 130 (26) , 266501
Top Cited PapersFermion 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 (QCPs) [W. Jiang et al., arXiv:2209.07103]. Here we study, by means of large-scale quantum Monte Carlo simulation, the scaling behavior of the 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.
- 4 April 2023
- Published by American Physical Society (APS) in Physical Review B
- Vol. 107 (16) , 165104
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.
- 4 April 2023
- Published by American Physical Society (APS) in Physical Review B
- Vol. 107 (16) , 165104
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.
- 23 February 2022
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 128 (8) , 087201
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 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 toward 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 are 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.- 23 February 2022
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 128 (8) , 087201
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 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 toward 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 are 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.