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Condensed Matter Seminar

Fall 2022

Seminar Time:  Wednesdays, 10:20-11:10 AM
Location: IAMM 147 unless noted as Virtual
Zoom for Virtual Seminars: https://tennessee.zoom.us/j/95144505179


Date Speaker Title Host

August 24

Seminar Introduction

 

 

August 31

Hatem Barghathi
Postdoc at UT

Balls and Walls: A Compact Unary Coding for Bosonic States

Ruixing Zhang

September 7

Peizhi Mai
Postdoc at UIUC

Topological Mott insulator

Steve Johnston

September 14
VIRTUAL

Lingyuan Kong
AWS Quantum Postdoctoral Fellow at Caltech

Majorana Modes in Iron-Based Superconducting Vortex

Ruixing Zhang

September 21

Nitin Kaushal
Postdoc at ORNL

Magnetic Ground States of Honeycomb Lattice Wigner Crystals

Elbio Dagotto

September 28

Rubem Mondaini
Assistant Professor at Beijing Computational Science Research Center

Overcoming Exponential Walls in Quantum Many-Body Systems

Steve Johnston

October 5

Pouyan Ghaemi
Associate Professor at CUNY

Quantum Algorithm to Realize and Study Fractional Hall States and Their Dynamics on Near-Term Quantum Computers: A Tabletop Experiment on Quantum Gravity

Ruixing Zhang

October 12

Brenda Rubenstein
Associate Professor at Brown University

TBA

Adrian Del Maestro

October 19
VIRTUAL

Shenglong Xu
Research Assistant Professor at Texas A&M University

TBA

Ruixing Zhang

October 26
VIRTUAL

Alex Frano
Assistant Professor at UCSD

TBA

Jian Liu

November 2

Hyungkook Choi
Associate Professor at Jeonbuk National University

TBA

Joon Sue Lee

November 9

Yongtian Luo
Johns Hopkins Postdoc

TBA

Maxim Lavrentovich

November 16

Jiabin Yu
Moore Postdoc Fellow at Princeton University

TBA

Ruixing Zhang

November 30
VIRTUAL

Hyunsoo Kim
Assistant Professor at Missouri S&T

TBA

Joon Sue Lee


Abstracts

Balls and Walls: A Compact Unary Coding for Bosonic States

Discrete lattice models play an essential role in the understanding of quantum phenomena, but their exact numerical solution is hindered by the exponentially growing size of the underlying Hilbert space. Such difficulty is more pronounced in the case of bosons due to the lack of any occupation restrictions as opposed to fermionic or even spin models. To ease some of the difficulties, we introduce a unary coding of bosonic occupation states based on the famous balls and walls counting for the number of configurations of N indistinguishable particles on L distinguishable sites. Each state is represented by an integer with a human-readable bit string that has a compositional structure allowing for the efficient application of operators that locally modify the number of bosons. By exploiting translational and inversion symmetries, we identify a speedup factor of order L over current methods when generating the basis states of bosonic lattice models. The unary coding is applied to a one-dimensional Bose-Hubbard Hamiltonian with up to L = N = 20, and the time needed to generate the ground-state block is reduced to a fraction of the diagonalization time. A widely adopted approximation in exact diagonalization as well as in the Density Matrix Renormalization Group is to restrict the bosonic occupation numbers to only a few bosons per lattice site. While the relative errors under this approximation in many observables including the energy or local particle number fluctuations could be negligible, we report that imposing such restrictions could have drastic effects on quantum information measures such as particle and accessible (symmetry resolved) entanglement entropies. Specifically, we show that for the ground state symmetry resolved entanglement, variational approaches restricting the local bosonic Hilbert space could result in an error that scales with system size.


Topological Mott insulator

While the recent advances in topology have led to a classification scheme for electronic bands described by the standard theory of metals, a similar scheme has not emerged for strongly correlated systems such as Mott insulators in which a partially filled band carries no current. By including interactions in the topologically non-trivial Haldane model, we show that a quarter-filled state emerges with a non-zero Chern number provided the interactions are sufficiently large. We establish this result first analytically by solving exactly a model in which interactions are local in momentum space. The exact same results obtain also for the Hubbard interaction, lending credence to the claim that both interactions lie in the same universality class. From the simulations with determinantal quantum Monte Carlo, we find that the spin structure at quarter filling is ferromagnetic for the topologically non-trivial case. We later generalize this study to quantum spin Hall system and obtain the quantum spin Hall Mott insulator.


Majorana Modes in Iron-Based Superconducting Vortex

VIRTUAL

Iron-based superconducting vortex is emerging as a promising platform for Majorana quasiparticle. After four-year intensive studies, substantial achievements have been made on several compounds, including Fe(Te,Se), (Li,Fe)OHFeSe, CaKFe4As4and LiFeAs. For example, the discovery of integer series of quantized bound states manifests nontrivial topology of vortex zero mode, promises a hope to the field of Majorana research. In this talk, I will depict the main profile of this emerging Majorana platform, on the aspects of materials, bound states, experimental configurations, and etc. Its advantages on physics study and the major controversies owing to the practical diversity will be discussed in short. The systematic investigations accomplished on this platform is promoting the entrance to a second-phase research for manipulating Majorana zero modes in an iron-based superconductor device.

Reference:

  • Kong & Ding. arXiv: 2108.12850 (2021) [Review]
  • Wang et al. Science 360, 182 (2018)
  • Kong et al. Nat. Phys. 15, 1181 (2019)
  • Kong et al. Nat. Commun. 12, 4146 (2021)
  • Liu et al. arXiv: 2111.03786 (2021)

Magnetic Ground States of Honeycomb Lattice Wigner Crystals

In recent years, moiré materials constructed using two layers of transition metal dichalcogenides have been used to simulate the Hubbard model on triangular lattice procuring strongly correlated physics in half-filled (n=1) flat bands. Lattice Wigner crystal states, at other fractional fillings like n=2/3, 1/2, and 1/3, are also stabilized by long-range Coulomb interactions in these two-dimensional triangular moiré lattices. Recent ab-initio work on the Gamma-valley transition metal dichalcogenide homobilayers unveiled effective moiré honeycomb lattices near the Fermi level. We employ large-scale unrestricted Hartree-Fock techniques to unveil the magnetic phase diagrams of honeycomb lattice Wigner crystals. For the three lattice filling factors with the largest charge gaps, n = 2/3, 1/2, 1/3, the magnetic phase diagrams contain multiple phases, including ones with non-collinear and non-coplanar spin arrangements. We discuss magnetization evolution with the external magnetic field, which has potential as an experimental signature of these exotic spin states. Our theoretical results could potentially be validated in moiré materials formed from group VI transition metal dichalcogenide twisted homobilayers.


Overcoming Exponential Walls in Quantum Many-Body Systems

In this talk I plan to provide an overview of how limitations inherent to interacting quantum systems present as a roadblock to their study in classical computers. Nonetheless, ingenious methods can be used such that useful information can yet be obtained in the face of these impediments. In particular, I will discuss the emergence of the sign problem in quantum Monte Carlo simulations, and argue that besides being a mere nuisance, one can use it as a tool to investigate quantum criticality. Furthermore, I will show that using metrics associated to the Monte Carlo sampling, including the mean distance traveled in the hyper-dimensional space of configurations, constitute as powerful means to diagnostic the onset of ordered behavior.


Quantum Algorithm to Realize and Study Fractional Hall States and Their Dynamics on Near-Term Quantum Computers: A Tabletop Experiment on Quantum Gravity

Intermediate-scale quantum technologies provide unprecedented opportunities for scientific discoveries while posing the challenge of identifying important problems that can take advantage of them through algorithmic innovations. Fractional Hall systems which are one class of correlated electron systems with many interesting and puzzling properties. In this talk I present an efficient quantum algorithm to generate an equivalent many-body state to Laughlin's ν=1/3 fractional quantum Hall state on a digitized quantum computer. Our algorithm only uses quantum gates acting on neighboring qubits in a quasi-one-dimensional setting, and its circuit depth is linear in the number of qubits. I then present another quantum algorithm to generate and study out of equilibrium properties of fractional Hall state. Such features reveals novel geometric aspects of fractional Hall states which mimics gravitons.

References:
[1] PRX Quantum 1, 020309 (2020)
[2] Phys. Rev. Lett. 129, 056801 (2022)


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