I am an associate member of IASTU, working on theoretical many-body physics.
Research
(updated Sep 2021)
I am broadly interested in strongly correlated systems and topological quantum states. My research is mainly focused on numerical investigation of low dimensional quantum systems.
Numerical study of strongly correlated systems
For strongly correlated systems in general, analytical approaches are often limited, if not nonexistent. Thus numerical methods serve as an important tool, both to support analytical argument and conjectures, and to uncover and inspire new ideas. A significant example of the latter is the density matrix renormalization group (DMRG) [Schollwock2011], which along with other works underscores the entanglement entropy as a relevant parameter in identifying topological order and naturally generalizes to other tensor network constructions. Two classes of numerical methods, exact diagonalization (ED) and matrix product state (MPS) based algorithms including DMRG and time-evolving block decimal (TEBD) [Paecker2019], are extensively exploited in my previous works. Despite being limited by the exponential growth of the Hilbert space, ED gives precise information and is applicable to systems that numerically converge poorly otherwise. Indeed, in Sachdev-Ye-Kitaev (SYK) [Sachdev1993,Kitaev2015,Maldacena2016] like models, the all-to-all nature of the interaction and the highly entangled ground state discourage an MPS ansatz, but enable an excellent approximation of the thermodynamic limit with a moderate system size using ED. In [Lantagne2018], we exploit this advantage and map out a phase diagram of a family of generalized SYK models, by characterizing properties including the spectral function, the level statistics, and the out-of-time-order correlator (OTOC). In [Li2019], supersymmetry (SUSY) is identified from a combination of ED and DMRG calculations.
For (quasi) 1D systems with local interactions, the area law dictates that the entanglement entropy of the ground state grows at most logarithmically with regard to the system size, and therefore the MPS is capable of approximating such states with high precision while using reasonable computation resources. Combining DMRG simulations with mean field and conformal field theoretical (CFT) arguments, we construct in [Li2020] a topological phase in 2D with tricritical Ising modes on its edges. I also implemented an MPS routine that fully incorporates the SU(2) symmetry, thus significantly reducing the computational cost compared to the usual U(1) realization for several ongoing projects.
Emergent high-energy phenomena in condensed matter physics
Recent decades have witnessed a flourishing of high-energy ideas realized in condensed matter systems, from elusive particles like Majorana and Weyl fermions to deep principles including the AdS-CFT duality. One topic of great interest to me is supersymmetry (SUSY). In the condensed matter literature, there are mainly two approaches that lead to SUSY – either constructing an explicit SUSY Hamiltonian and asking whether the ground states spontaneously break the symmetry, or looking for ground states in non-SUSY systems that are described by a SUSY field theory. We explore the first approach in [Li2019] in a Majorana model on the kagome lattice, and the second in [Li2020] as a coupled wire construction of the Grover-Sheng-Vishwanash model [Grover2014].
Quantum chaos and dynamics
Another topic I have been focused on is quantum chaos. While its classical counterpart is formulated with differential equations, quantum dynamics of closed systems is described by unitary evolution, complicating an application of classical chaos ideas to the quantum regime. One quantity that has drawn significant research interests recently is the out-of-time-order correlator (OTOC), which is a generalization of the classical idea of “dependence of later time motion on the variance at the initial time”. From a quantum information point of view, OTOC characterizes how information is scrambled in the quantum system. The time dependence of OTOC further allows a definition of the quantum Lyapunov exponent, the classical counterpart of which plays a fundamental role in chaos theory. In [Lantagne2018], we calculate the OTOC in generalized SYK models and find similar behaviour as the original SYK model. In an ongoing project, we focus on the Heisenberg spin chains and calculate the OTOC with the SU(2) invariant TEBD mentioned above. We are able to map out the lightcone structure and extract the Lyapunov exponent for spin up to 5.
Short CV
Mar 2024 – now | Associate member | |
Tsinghua University | ||
Oct 2021 – Mar 2024 | Postdoc | |
Tsinghua University | ||
Supervisor: Prof. Hui Zhai | ||
Sep 2017 – Jul 2021 | PhD in Physics | |
University of British Columbia | ||
Supervisor: Prof. Marcel Franz | ||
Sep 2015 – Aug 2017 | MSc in Physics | |
University of British Columbia | ||
Supervisor: Prof. Marcel Franz | ||
Aug 2011 – Jul 2015 | BSc in Physics | |
Tsinghua University | ||
Supervisor: Prof. Li You & Prof. Meng Khoon Tey |
Publications
Also see Google Scholar.
- “Uncovering Emergent Spacetime Supersymmetry with Rydberg Atom Arrays”,
CL*, Shang Liu*, Hanteng Wang, Wenjun Zhang, Zi-Xiang Li, Hui Zhai, and Yingfei Gu,
arXiv:2407.08194. - “Numerical investigations of the extensive entanglement Hamiltonian in quantum spin ladders”,
CL, Xingyu Li, and Yi-Neng Zhou,
Quantum Front. 3, 9 (2024), arXiv:2311.01699. - “Reviving the Lieb–Schultz–Mattis Theorem in Open Quantum Systems”,
Yi-Neng Zhou*, Xingyu Li*, Hui Zhai, CL, and Yingfei Gu,
Natl. Sci. Rev. nwae287 (2024), arXiv:2310.01475,
highlighted in the Journal Club for Condensed Matter Physics. - “Euler–Chern correspondence via topological superconductivity”,
Fan Yang*, Xingyu Li*, and CL,
Phys. Rev. Res. 5, 033073 (2023), arXiv:2305.16113. - “G2 integrable point characterization via isotropic spin-3 chains”,
CL, Victor L. Quito, Dirk Schuricht, and Pedro L. S. Lopes,
Phys. Rev. B 108, 165123 (2023), arXiv:2305.03072. - “Frustration-induced itinerant ferromagnetism of fermions in optical lattices”,
CL, Ming-Gen He, Chang-Yan Wang, and Hui Zhai,
Phys. Rev. B 109, 165131 (2024), arXiv:2305.01682. - “Gauge theory description of Rydberg atom arrays with a tunable blockade radius”,
Yanting Cheng and CL,
Phys. Rev. B 107, 094302 (2023), arXiv:2212.14644. - “Lee–Yang zeros in the Rydberg atoms”,
CL and Fan Yang,
Front. Phys. 18, 22301 (2023), arXiv:2203.16128. - “Variational approach to quantum spin liquid in a Rydberg atom simulator”,
Yanting Cheng, CL, and Hui Zhai,
New J. Phys. 25, 033010 (2023), arXiv:2112.13688. - “The case of SU(3) criticality in spin-2 chains”,
CL, Victor L. Quito, Eduardo Miranda, Rodrigo Pereira, Ian Affleck, and Pedro L. S. Lopes,
Phys. Rev. B 105, 085140 (2022), arXiv:2108.10329. - “Coupled wire construction of a topological phase with chiral tricritical Ising edge modes”,
CL, Hiromi Ebisu, Sharmistha Sahoo, Yuval Oreg, and Marcel Franz,
Phys. Rev. B 102, 165123 (2020), arXiv:2008.04438. - “Supersymmetry in an interacting Majorana model on the kagome lattice”,
CL*, Étienne Lantagne-Hurtubise*, and Marcel Franz,
Phys. Rev. B 100, 195146 (2019), arXiv:1811.06104. - “Majorana-Hubbard model on the honeycomb lattice”,
CL and Marcel Franz,
Phys. Rev. B 98, 115123 (2018), arXiv:1806.06092. - “Family of Sachdev-Ye-Kitaev models motivated by experimental considerations”,
Étienne Lantagne-Hurtubise*, CL*, and Marcel Franz,
Phys. Rev. B 97, 235124 (2018), arXiv:1803.07197.
The asterisk (*) denotes equal contribution.
More about me
My name is written as 李成疏 in Chinese and it is pronounced as /li21(4) ʈ͡ʂʰɤŋ35 ʂu55/. (Not familiar with these symbols? They are called IPA and can be used to describe any language in the world! Did you know that Mandarin, like many other languages in the world, is a tonal language?)
I was born in Zhangjiakou, a city near Beijing, and moved to Shanghai at the age of 5. I went to Beijing for my undergrad and went to grad school in Vancouver.
Apart from physics, I am interested in linguistics, language learning (français and 日本語), classical music, and animes.
Contact
lichengshu272(at)gmail(dot)com