Research fields

I have long been engaged in research on equilibrium and non-equilibrium statistical physics and condensed matter theory, especially on phase transitions, critical phenomena, and topological properties in many-body systems. I have published many papers in related fields, including Phys. Rev. Lett, Phys. Rev A/B/E etc. (For details, please see the introduction video in Koushare: https://m.koushare.com/lives/room/950111):

Method

• Numerical: Quantum Monte Carlo, density matrix renormalization group and exact diagonalization methods
• Analytical: exact solvable model, perturbative renormalization group, Bosonization and conformal field theory, etc.

Equilibrium quantum phase transition

Universality is one of the most important concepts in physics. However, due to the existence of different universal classes, phase transitions and critical phenomena have always been basic issues in statistical physics, condensed matter physics, and even the entire physics research.

Phase change is the transformation that occurs between different phase of matters (the transition point is called critical point, we generally care about the second-order or continuous phase transition point). When the phase transition is mainly driven by thermal fluctuations, it is called a classical (thermal) phase transition; when the phase change is mainly driven by quantum fluctuations (Heisenberg uncertainty principle), it is called a quantum phase change (at absolute zero temperature, consider transition between system ground states).

The classical phase transition (spontaneous symmetry breaking theory) was established by Landau-Ginzberg-Wilson in the last century (also known as the Landau-Ginzberg-Wilson paradigm). According to the quantum-classical correspondence, a d-dimensional quantum system can equivalent to a classical system of d+1 dimensions. In this sense, the Landau-Ginzberg-Wilson spontaneous symmetry breaking theory has become the "standard theory" in the field of phase transitions in physics [1,2] (also known as the conventional quantum critical point).

However, since the 1980s, physicists have discovered that some phase transitions cannot be understood by the Landau-Ginzberg-Wilson paradigm, such as the KT phase transition induced by topological defects (2016 Nobel Prize). Among them, the introduction of topological concepts has greatly promoted the development of condensed matter physics and statistical physics (another very big progress is topological quantum matter states, which exceeds the framework of Landau-Fermi liquid theory). Therefore, a core issue in modern condensed matter physics and statistical physics is to understand the relationship between phase transitions beyond the Landau-Ginzberg-Wilson paradigm (called unconventional quantum critical points, such as deconfinement quantum critical points, symmetric mass generation phase transitions, etc.) and beyond. Novel quantum states of matter based on Landau-Fermi liquid theory (such as symmetry-protected topological phases, spin liquids, etc.).

[1] XJY, Peng-Lu Zhao, Shao-Kai Jian, and Zhiming Pan, Phys. Rev. B 105, 205140 (2022)

[2] XJY, and Zhiming Pan, to be appear

[3] Hao-Long Zhang, Pei-Rong Han, XJY*, et al. arXiv: 2407. 00903 (2024)

My works in equilibrium quantum phase transitions in the past few years mainly include:

1) When people generally discuss phase transitions, they do not consider the boundaries of the infinite system (bulk). When there is a boundary in the system, the boundary critical behavior is richer than the bulk, which is called surface critical behavior. Similar to how topological invariants (such as Chen number, Z2 topological number, etc.) can classify symmetry-protected topological phases with energy gaps, my collaborators and I proposed for the first time that conformal boundary conditions and corresponding surface critical behaviors can be used as "topological invariants" in topological quantum critical states [1,2,3,4,5,6]. In addition, we also propose novel bulk-boundary correspondences in gapless quantum critical states for the first time. Our work reveals profound connections between surface criticality, gapless symmetry-protected topological phases, symmetry-enriched quantum critical states, and other frontier areas of modern condensed matter theory.

[1] XJY, Rui-Zhen Huang, Hong-Hao Song, Limei Xu, Chengxiang Ding, and Long Zhang, Phys. Rev. Lett 129, 210601 (2022)

[2] XJY, Sheng Yang, Hai-Qing Lin, and Shao-Kai Jian, Phys. Rev. Lett. 133, 026601 (2024)

[3] XJY, and Wei-Lin Li, Phys. Rev. B 110, 045119 (2024)

[4] Wen-Hao Zhong (undergraduate), Wei-Lin Li, Yong-Chang Chen (undergraduate), and XJY, arXiv: 2403.11880 (2024) (Accepted by Phys. Rev. A)

[5] Hao-Long Zhang, Han-Ze Li, Sheng Yang, and XJY, Phys. Rev. A 109,062226 (2024)

[6] Sheng Yang, Hai-Qing Lin, and XJY, arXiv: 2406.01974(2024)

2）Locality is a basic assumption in quantum field theory. When there are some non-local tems in the system, some unexpected and novel physical phenomena may appear. Long-range interaction is a typical non-local term. The development of quantum simulation technology in recent years (such as ion traps, Rydberg atomic arrays [1], etc.) has made studying the physics of long-range interaction systems no longer a matter of paper. Long-range interactions will change the "fundamental laws" of traditional condensed matter physics and statistical physics, such as the failure of quantum-classical correspondence, the destruction of the Mermin-Wagner theorem, etc. For quantum critical behavior, even for conventional quantum critical points, the introduction of long-range interactions will induce new long-range universality classes [2]. For unconventional quantum critical points, such as deconfined quantum critical points, the introduction of long-range interactions will transform the second-order continuous phase transition into a first-order phase transition. What is even more interesting is that the first-order phase transition will exhibit emergent symmetry at this time [3]. This beyond people traditional understanding of emergent symmetries in condensed matter physics (generally occurring at the second-order or continuous phase transition point).

[1]XJY, Sheng Yang, Jinbo Xu, and Limei Xu, Phys. Rev. B 106,165124 (2022)

[2] XJY, Chengxiang Ding, and Limei Xu, Phys. Rev. E 107, 054122 (2023)

[3] Sheng Yang, Zhiming Pan, Da-Chuan Lu, and XJY*, Phys. Rev. B 108, 245152 (2023)

3) Finding novel quantum phase of matter in strongly correlated quantum many-body systems is another fundamental task in condensed matter physics and statistical physics, and is of far-reaching significance for realizing topological quantum computing. My collaborators and I constructed the SU(N) SSH interacting fermion model on a square lattice for the first time [1]. Combining self-consistent average theory and large-scale quantum Monte Carlo simulations, we find that for the two limiting cases of large 𝑁 or small 𝑁 (𝑁 = 2, 3), the ground state of the model belongs to staggered valence bond solid and antiferromagnetic order respectively. Mutually. For the intermediate 𝑁 = 4, 5 case, on the one hand, the increase of 𝑁 causes the system to suppress the antiferromagnetic order and prefer the formation of valence-bond solid order. On the other hand, in the weak coupling region, the ground state is an staggered valence bond solid order due to the nesting of Fermi surfaces. On the contrary, in the strong coupling limit, the system evolves a columnar valence bond solid order. More unexpectedly, in the intermediate coupling region, there is an gapped Mott insulating phase between the staggered and columnar valence solid orders without any spontaneous symmetry breaking. Further combined with the Lieb-Schultz-Mattis theorem, we demonstrated that this intermediate phase is likely to be a quantum spin liquid with topological order. Our work not only provides a new model for studying the basic physics of quantum many-body systems, but also provides a feasible solution to find quantum spin liquids in practical systems.

[1] XJY, Shao-Hang Shi, Limei Xu, and Zi-Xiang Li, Phys. Rev. Lett. 132, 036704 (2024) (Editors's Suggestion)

Non-equilibrium quantum phase transition

For quantum phase transitions, we generally discuss transitions between equilibrium ground states. However, in recent years, more and more attention has been paid to the dynamical type of quantum phase transitions between non-ground states. In particular, quantum states and phase transitions are studied experimentally through dynamics. The most typical dynamical type of phase transition is disorder, quasi-periodic [1,2]-induced Anderson localization phase transition (or many-body localization), or even disorder-free many-body localization [3] . On the one hand, analogous to the singularity of free energy in temperature in classical statistical physics, a thermodynamical phase transition will occur. Then if a special "free energy" appears singular in time, a dynamic quantum phase transition will occur [4].

On the other hand, the interplay of quantum information and statistical physics has made people particularly interested in the transition between different entanglement laws (i.e., entanglement phase transition). Entanglement phase transition originates from the quantum circuit. The unitary evolution of the quantum state will enhance the entanglement of the system, while measuring the quantum state will reduce the entanglement of the system. The competition between unitary evolution and measurement therefore results in rich dynamically entangled phase transitions. In addition, dynamical phase transitions also occur in open quantum many-body systems. When we perform time-dependent evolution of the density matrix of the system through the Lindblad equation, if we perform post-selection and discard the quantum jump operator, we can obtain an effective non-Hermitian Hamiltonian [5]. There are very few studies on quantum critical behavior in non-Hermitian systems, especially non-Hermitian quantum many-body systems. My collaborators and I developed for the first time a set of efficient quantum Monte Carlo algorithms for special non-Hermitian quantum many-body systems (with PT symmetry) [6], and discovered the counterintuitive non-Hermitian enhanced antiferromagnetism and emergent Hermiticity at quantum critical points.

The problem of non-equilibrium quantum phase transition is very challenging in both quantum and classical many-body systems, but the physics is rich and interesting, and leaves a lot of room for young people to explore. It is a promising research direction.

[1] Shan-Zhong Li, XJY*(The first corresponding author), and Zhi Li, Phys. Rev. B 109. 024306 (2024)

[2] Shan-Zhong Li, XJY, Shi-Liang Zhu, and Zhi Li, Phys. Rev. B 108, 094209 (2023)

[3] Han-Ze Li, XJY*(co-first author), and Jian-Xin Zhong, Phys. Rev. A 108, 043301 (2023)

[4] XJY, Phys. Rev. A 108,062215 (2023)

[5] Zheng-Xin Guo, XJY*(co-first author), Xi-Dan Hu, and Zhi Li, Phys.Rev.A.105.053311(2022)

[6] XJY, Zhiming Pan, Limei Xu, and Zi-Xiang Li, Phys. Rev. Lett. 132. 116503 (2024)

All papers：https://www.researchgate.net/profile/Xue-Jia-Yu

Faculty page:

http://itlab.fzu.edu.cn/gzl/ZhuanJi/TeacherInfo2.aspx?No=T23086

Zhihu ID:Sugar Yu and bilibili:精力旺盛的subir

Welcome to follow the video recording and broadcasting on bilibili of the Quantum Matter Seminar @FZU organized by me (basically once a month, both online and onsite):

https://space.bilibili.com/196173388/channel/seriesdetail?sid=3050065&ctype=0

Collaborators include (but are not limited to)：