Recently,quantum simulation of low-dimensional lattice gauge theories(LGTs)has attracted many interests,which may improve our understanding of strongly correlated quantum many-body systems.Here,we propose an implement...Recently,quantum simulation of low-dimensional lattice gauge theories(LGTs)has attracted many interests,which may improve our understanding of strongly correlated quantum many-body systems.Here,we propose an implementation to approximate Z;LGT on superconducting quantum circuits,where the effective theory is a mixture of a LGT and a gauge-broken term.By using matrix product state based methods,both the ground state properties and quench dynamics are systematically investigated.With an increase of the transverse(electric)field,the system displays a quantum phase transition from a disordered phase to a translational symmetry breaking phase.In the ordered phase,an approximate Gauss law of the Z;LGT emerges in the ground state.Moreover,to shed light on the experiments,we also study the quench dynamics,where there is a dynamical signature of the spontaneous translational symmetry breaking.The spreading of the single particle of matter degree is diffusive under the weak transverse field,while it is ballistic with small velocity for the strong field.Furthermore,due to the emergent Gauss law under the strong transverse field,the matter degree can also exhibit confinement dynamics which leads to a strong suppression of the nearest-neighbor hopping.Our results pave the way for simulating the LGT on superconducting circuits,including the quantum phase transition and quench dynamics.展开更多
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 ...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.展开更多
We systematically test the performance of several Monte Carlo update schemes for the(2+1)d XY phase transition of quantum rotor model.By comparing the local Metropolis(LM),LM plus over-relaxation(OR),Wolff-cluster(WC)...We systematically test the performance of several Monte Carlo update schemes for the(2+1)d XY phase transition of quantum rotor model.By comparing the local Metropolis(LM),LM plus over-relaxation(OR),Wolff-cluster(WC),hybrid Monte Carlo(HM),hybrid Monte Carlo with Fourier acceleration(FA)schemes,it is clear that among the five different update schemes,at the quantum critical point,the WC and FA schemes acquire the smallest autocorrelation time and cost the least amount of CPU hours in achieving the same level of relative error,and FA enjoys a further advantage of easily implementable for more complicated interactions such as the long-range ones.These results bestow one with the necessary knowledge of extending the quantum rotor model,which plays the role of ferromagnetic/antiferromagnetic critical bosons or Z_(2)topological order,to more realistic and yet challenging models such as Fermi surface Yukawa-coupled to quantum rotor models.展开更多
基金supported by China Postdoctoral Science Foundation(Grant No.2020T130643)the Fundamental Research Funds for the Central Universities,and the National Natural Science Foundation of China(Grant No.12047554)+5 种基金support from the National Key Research and Development Program of China(Grant No.2016YFA0300502)the Research Grants Council of Hong Kong SAR China(Grant No.17303019)support from the National Key R&D Program of China(Grant Nos.2016YFA0302104 and 2016YFA0300600)the National Natural Science Foundation of China(Grant Nos.11774406 and 11934018)Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDB28000000)Beijing Academy of Quantum Information Science(Grant No.Y18G07)。
文摘Recently,quantum simulation of low-dimensional lattice gauge theories(LGTs)has attracted many interests,which may improve our understanding of strongly correlated quantum many-body systems.Here,we propose an implementation to approximate Z;LGT on superconducting quantum circuits,where the effective theory is a mixture of a LGT and a gauge-broken term.By using matrix product state based methods,both the ground state properties and quench dynamics are systematically investigated.With an increase of the transverse(electric)field,the system displays a quantum phase transition from a disordered phase to a translational symmetry breaking phase.In the ordered phase,an approximate Gauss law of the Z;LGT emerges in the ground state.Moreover,to shed light on the experiments,we also study the quench dynamics,where there is a dynamical signature of the spontaneous translational symmetry breaking.The spreading of the single particle of matter degree is diffusive under the weak transverse field,while it is ballistic with small velocity for the strong field.Furthermore,due to the emergent Gauss law under the strong transverse field,the matter degree can also exhibit confinement dynamics which leads to a strong suppression of the nearest-neighbor hopping.Our results pave the way for simulating the LGT on superconducting circuits,including the quantum phase transition and quench dynamics.
基金support from the National Key Research and Development Program of China(Grant No.2016YFA0300502)the Research Grants Council of Hong Kong SAR China(Grant Nos.17303019 and 17301420)supported by Priority Academic Program Development(PAPD)of Jiangsu Higher Education Institutions,China。
文摘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.
基金the supports from the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDB33000000)the RGC of Hong Kong SAR of China(Grant Nos.17303019,17301420,and AoE/P-701/20)。
文摘We systematically test the performance of several Monte Carlo update schemes for the(2+1)d XY phase transition of quantum rotor model.By comparing the local Metropolis(LM),LM plus over-relaxation(OR),Wolff-cluster(WC),hybrid Monte Carlo(HM),hybrid Monte Carlo with Fourier acceleration(FA)schemes,it is clear that among the five different update schemes,at the quantum critical point,the WC and FA schemes acquire the smallest autocorrelation time and cost the least amount of CPU hours in achieving the same level of relative error,and FA enjoys a further advantage of easily implementable for more complicated interactions such as the long-range ones.These results bestow one with the necessary knowledge of extending the quantum rotor model,which plays the role of ferromagnetic/antiferromagnetic critical bosons or Z_(2)topological order,to more realistic and yet challenging models such as Fermi surface Yukawa-coupled to quantum rotor models.