Contributor info: Dr Pengfei Zhang

Ruihua Fan, Pengfei Zhang, Yingfei Gu

SciPost Phys. 15, 249 (2023) · published 20 December 2023 | Toggle abstract · pdf

We generalize a real-space Chern number formula for gapped free fermions to higher orders. Using the generalized formula, we prove recent proposals for extracting thermal and electric Hall conductance from the ground state via the entanglement Hamiltonian in the special case of non-interacting fermions, providing a concrete example of the connection between entanglement and topology in quantum phases of matter.

Tian-Gang Zhou, Pengfei Zhang

SciPost Phys. 15, 108 (2023) · published 21 September 2023 | Toggle abstract · pdf

Quench dynamics of fermionic superfluids are an active topic both experimentally and theoretically. Using the BCS theory, such non-equilibrium problems can be reduced to nearly independent spin dynamics, only with a time-dependent mean-field pairing term. This results in persisting oscillations of the pairing strength in certain parameter regimes. However, experiments have observed that the oscillations decay rapidly when the interaction becomes strong, such as in the unitary Fermi gas [Phys. Rev. Res. 3, 023205 (2021)]. Theoretical analysis on this matter is still absent. In this work, we construct an SYK-like model to analyze the effect of strong interactions in a one-dimensional BCS system. We employ the large-$N$ approximation and a Green's function-based technique to solve the equilibrium problem and quench dynamics. Our findings reveal that a strong SYK interaction suppresses the pairing order. Additionally, we verify that the system quickly thermalizes with SYK interactions, whether it involves intrinsic pairing order or proximity effect, resulting in a rapid decay of the oscillation strength. The decay rates exhibit different scaling laws against SYK interaction, which can be understood in terms of the Boltzmann equation. This work represents a first step towards understanding the attenuating dynamics of strongly interacting fermionic superfluids.

Pengfei Zhang

SciPost Phys. Core 5, 010 (2022) · published 7 March 2022 | Toggle abstract · pdf

Quantum emitters, particularly atomic arrays with subwavelength lattice constant, have been proposed to be an ideal platform for studying the interplay between photons and electric dipoles. In this work, motivated by the recent experiment [1], we develop a microscopic quantum treatment using annihilation and creation operator of atoms in deep optical lattices. Using a diagrammatic approach on the Keldysh contour, we derive the cooperative scattering of the light and obtain the general formula for the $S$ matrix. We apply our method to study the trapping effect, which is beyond previous treatment with spin operators. If the optical lattices are formed by light fields with magical wavelength, the result matches previous results using spin operators. When there is a mismatch between the trapping potentials for atoms in the ground state and the excited state, atomic mirrors become imperfect, with multiple resonances in the optical response. We further study the effect of recoil for large but finite trapping frequency. Our results are consistent with existing experiments.

Chunxiao Liu, Pengfei Zhang, Xiao Chen

SciPost Phys. 10, 048 (2021) · published 23 February 2021 | Toggle abstract · pdf

We construct a series of one-dimensional non-unitary dynamics consisting of both unitary and imaginary evolutions based on the Sachdev-Ye-Kitaev model. Starting from a short-range entangled state, we analyze the entanglement dynamics using the path integral formalism in the large $N$ limit. Among all the results that we obtain, two of them are particularly interesting: (1) By varying the strength of the imaginary evolution, the interacting model exhibits a first order phase transition from the highly entangled volume law phase to an area law phase; (2) The one-dimensional free fermion model displays an extensive critical regime with emergent two-dimensional conformal symmetry.

Pengfei Zhang, Yingfei Gu

SciPost Phys. 9, 079 (2020) · published 23 November 2020 | Toggle abstract · pdf

We study the quantum dynamics of Bose-Einstein condensates when the scattering length is modulated periodically or quasi-periodically in time within the Bogoliubov framework. For the periodically driven case, we consider two protocols where the modulation is a square-wave or a sine-wave. In both protocols for each fixed momentum, there are heating and non-heating phases, and a phase boundary between them. The two phases are distinguished by whether the number of excited particles grows exponentially or not. For the quasi-periodically driven case, we again consider two protocols: the square-wave quasi-periodicity, where the excitations are generated for almost all parameters as an analog of the Fibonacci-type quasi-crystal; and the sine-wave quasi-periodicity, where there is a finite measure parameter regime for the non-heating phase. We also plot the analogs of the Hofstadter butterfly for both protocols.

Pengfei Zhang, Chunxiao Liu, Xiao Chen

SciPost Phys. 8, 094 (2020) · published 26 June 2020 | Toggle abstract · pdf

The Sachdev-Ye-Kitaev model is an $N$-modes fermionic model with infinite range random interactions. In this work, we study the thermal R\'enyi entropy for a subsystem of the SYK model using the path-integral formalism in the large-$N$ limit. The results are consistent with exact diagonalization [1] and can be well approximated by thermal entropy with an effective temperature [2] when subsystem size $M\leq N/2$. We also consider generalizations of the SYK model with quadratic random hopping term or $U(1)$ charge conservation.