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Chin. Phys. B, 2022, Vol. 31(2): 020304    DOI: 10.1088/1674-1056/ac380e
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Quantum simulation of lattice gauge theories on superconducting circuits: Quantum phase transition and quench dynamics

Zi-Yong Ge(葛自勇)1,2, Rui-Zhen Huang(黄瑞珍)3,†, Zi-Yang Meng(孟子杨)1,4,5, and Heng Fan(范桁)1,2,4,6,‡
1 Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China;
2 School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China;
3 Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China;
4 Songshan Lake Materials Laboratory, Dongguan 523808, China;
5 Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Hong Kong SAR, China;
6 CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China
Abstract  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 $\mathbb{Z}_2$ 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 $\mathbb{Z}_2$ 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.
Keywords:  quantum simulation      superconducting circuits      lattice gauge theories  
Received:  16 August 2021      Revised:  28 September 2021      Accepted manuscript online:  10 November 2021
PACS:  03.67.-a (Quantum information)  
  05.30.Rt (Quantum phase transitions)  
  11.15.Ha (Lattice gauge theory)  
Fund: The DMRG and TEBD calculations are carried out with TeNPy Library.[50] R.Z.H is 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). Z. Y. M acknowledges support from the National Key Research and Development Program of China (Grant No. 2016YFA0300502) and the Research Grants Council of Hong Kong SAR China (Grant No. 17303019). H. F acknowledges 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), and Beijing Academy of Quantum Information Science (Grant No. Y18G07).
Corresponding Authors:  Rui-Zhen Huang, Heng Fan     E-mail:;

Cite this article: 

Zi-Yong Ge(葛自勇), Rui-Zhen Huang(黄瑞珍), Zi-Yang Meng(孟子杨), and Heng Fan(范桁) Quantum simulation of lattice gauge theories on superconducting circuits: Quantum phase transition and quench dynamics 2022 Chin. Phys. B 31 020304

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