Condensed Matter

When an interacting quantum many-body system is cooled down to its ground state, there can be discrete "topological invariants" that characterize the properties of such ground states. This leads to the concept of "topological phases of matter" distinguished by these topological invariants. Experimental manifestations of these topological phases of matter include the integer and fractional quantum Hall effect, as well as topological insulators.

In this talk, after a general overview of topological phases of matter, I will explain how to define topological invariants that are specific to the ground states of regular crystals, i.e. systems that are periodic in space. I will discuss the physical manifestations of the resulting "crystalline topological phases", including implications for the properties of crystalline defects such as dislocations and disclinations. Then, I will explain how these ideas can be generalized to quasicrystals, which are a different class of materials that have long-range spatial order without exact periodicity. These ideas ultimately lead to a general classification principle for crystalline and quasicrystalline topological phases of matter.

I will first give a brief overview of my research in the field of out-of-equilibrium quantum many-
body physics, ranging from the theory of many-body localization, to the recent application of Tensor

Processing Units for accelerating simulations of quantum dynamics. I’ll then focus on (1) the

experimental observation and theoretical explanation of subdiffusive dynamics in a “tilted” Fermi-
Hubbard system [PRX 10, 011042 (2020)], and (2) a “freezing” phase transition between weak and

strong ergodicity breaking in systems with particles that are immobile by themselves, but undergo
coordinated pair hopping [PRB 101, 214205 (2020)]. These topics contain the common thread of
either an emergent or microscopic conservation of the dipole moment (center of mass of the particle
distribution), and I will provide simple pictures for how this leads to the subdiffusion and ergodicity
breaking.

In thermal equilibrium, 1d bosonic systems (e.g. spin- or qubit- chains) cannot support intrinsically topological phases without symmetry protection. For example, the edge states of the Haldane spin chain are fragile to magnetic fields, in contrast to the absolutely stable Majorana edge states of a topological superconducting wire of fermionic electrons. This fragility is a serious drawback to harnessing topological edge states as protected quantum memories in existing AMO and qubit platforms for quantum simulation and information processing. In this talk, I will present evidence for a non-equilibrium topological phase of quasiperiodically-driven trapped ion chains, that exhibits topological edge states that are protected purely by emergent dynamical symmetries that cannot be broken by microscopic perturbations. This represents both the first experimental realization of a non-equilibrium quantum phase, and the first example of a 1d bosonic topological phase that does not rely on symmetry-protection.

Conformal field theories (CFTs) are ubiquitous in theoretical physics as fixed points of renormalization, descriptions of critical systems and more. In these theories the conformal symmetry is a powerful tool in the computation of correlation functions, especially in 2 dimensions where the conformal algebra is infinite. Discretization of field theories is another powerful tool, where the theory on the lattice is both mathematically well-defined and easy to put on a computer. In this talk I will outline how these are combined using a discrete version of the 2d conformal algebra that acts in lattice models. I will also discuss recent work on convergence of this discretization, as well as on applications to non-unitary CFTs that appear in descriptions of problems of interest in condensed matter physics such as polymers, percolation and disordered systems.

Zoom Link: https://pitp.zoom.us/j/95048143778?pwd=N1hhVHlsZThVYzBWTy9CNlBTUHIydz09

I will introduce the notion of Pivot Hamiltonians, a special class of Hamiltonians that can be used to "generate" both entanglement and symmetry. On the entanglement side, pivot Hamiltonians can be used to generate unitary operators that prepare symmetry-protected topological (SPT) phases by "rotating" the trivial phase into the SPT phase. This process can be iterated: the SPT can itself be used as a pivot to generate more SPTs, giving a rich web of dualities. Furthermore, a full rotation can have a trivial action in the bulk, but pump lower dimensional SPTs to the boundary, allowing the practical application of scalably preparing cluster states as SPT phases for measurement-based quantum computation. On the symmetry side, pivot Hamiltonians can naturally generate U(1) symmetries at the transition between the aforementioned trivial and SPT phases. The sign-problem free nature of the construction gives a systematic approach to realize quantum critical points between SPT phases in higher dimensions that can be numerically studied. As an example, I will discuss a quantum Monte Carlo study of a 2D lattice model where we find evidence of a direct transition consistent with a deconfined quantum critical point with emergent SO(5) symmetry.

This talk is based on arXiv:2107.04019, 2110.07599, 2110.09512

Van der Waals heterostructures provide a rich venue for exotic moir\’e phenomena. In this talk, I will present a couple of unconventional examples beyond the celebrated twisted bilayer graphene. I will start by twisted bilayer of square lattice with staggered flux, which exhibits a continuum range of magic twisting angles where an exponential reduction of Dirac velocity and bandwidths occurs. Then I will discuss moir\’e magnetism arising from twisted bilayers of antiferromagnets and also ferromagnets. Despite the fact that the parent materials all exhibit collinear orderings, the bilayer system shows controllable emergent noncollinear spin textures. Time permitting, I will also discuss a theory for the potentially continuous metal-insulator transition with fractionalized electric charges in transition metal dichalcogenide moir\’e heterostructures.

Zoom Link: https://pitp.zoom.us/j/99322296758?pwd=WUNGcE1JS3FpZ1VxbklsSCtYTEJVdz09

Competition between unitary dynamics that scramble quantum information non-locally and local measurements that probe and collapse the quantum state can result in a measurement-induced entanglement phase transition. We introduce large-N Brownian hybrid circuits acting on clusters of qubits, which provide an analytically tractable model for measurement-induced criticality. The system is initially entangled with an equal sized reference, and the subsequent hybrid system dynamics either partially preserves or destroys this entanglement depending on the measurement rate. Our approach can access a variety of entropic observables, which are represented as a replica path integral with twisted boundary conditions. Saddle-point analysis reveals a second-order phase transition corresponding to replica permutation symmetry breaking below a critical measurement rate. The transition is mean-field-like and we characterize the critical properties near the transition in terms of a simple Ising field theory in 0+1 dimensions. By coupling the large-N clusters on a lattice, we also extend these solvable models to study the effects of power-law long-range couplings on measurement-induced phases. In one dimension, the long-range coupling is relevant for α<3/2, with α being the power-law exponent, leading to a nontrivial dynamical exponent at the measurement-induced phase transition. More interestingly, for α<1 the entanglement pattern receives a sub-volume correction for both area-law and volume-law phases. The volume-law phase for α<1 realizes a novel quantum error correcting code whose code distance scales as L^(2−2α).

References: 
[1] Phys. Rev. B 104, 094304 (2021), ArXiv:2104.07688.
[2] ArXiv:2109.00013.

Traditionally, magnetism in solids deals with ordering patterns of the electron magnetic dipole moment, as probed, for instance, via neutron diffraction. However, f-electron heavy fermion systems are well-known candidates for more complex forms of symmetry breaking, involving higher-order magnetic or electric multipoles. In this talk, I will discuss our recent theoretical proposal for Ising octupolar order in d-orbital systems, which appears to explain a wide range of experiments in certain 5d transition metal oxides with spin-orbit coupling. The proposed Ising ferro-octupolar order is shown to be linked to a type of orbital loop-current order. Deviations from cubic symmetry, via strain or surfaces, induces a transverse field on the octupolar order which can lead to surface quantum phase transitions, or transitions in thin films or in strained 3D crystals. We propose further experimental tests of our proposal.
 

I will discuss ongoing work on the robustness of symmetry protected topological (SPT) phases in open systems. By studying the evolution of non-local string order parameters, we find that one-dimensional SPT order is destabilized by couplings to the environment satisfying a weak symmetry condition that directly generalizes from closed systems. We introduce a stronger symmetry condition on channels that ensures SPT order is preserved. SPT phases of mixed states and their transformation under noisy channels is also discussed.

Many modern materials feature a “Planckian metal”: a phase of electronic quantum matter without quasiparticle excitations, and relaxation in a time of order Planck's constant divided by the absolute temperature. I will review recent progress in understanding such metals using insights from the Sachdev-Ye-Kitaev model of many-particle quantum dynamics. I will also note connections to progress in understanding the quantum nature of black holes.

Quantum spin liquids (QSL) are enigmatic phases of matter characterized by the absence of symmetry breaking and the presence of fractionalized quasiparticles. While theories for QSLs are now in abundance, tracking them down in real materials has turned out to be remarkably tricky. I will focus on two sets of studies on QSLs in three dimensional pyrochlore systems, which have proven to be particularly promising. In the first work, we analyze the newly discovered spin-1 pyrochlore compound NaCaNi2F7 whose properties we find to be described by a nearly idealized Heisenberg Hamiltonian [1]. We study its dynamical structure factor using molecular dynamics simulations, stochastic dynamical theory, and linear spin wave theory, all of which reproduce remarkably well the momentum dependence of the experimental inelastic neutron scattering intensity as well as its energy dependence (with the exception of the lowest energies) [2]. We apply many of the lessons learnt to Ce2Zr2O7 which has been recently shown to exhibit strong signatures of QSL behavior in neutron scattering experiments. Its magnetic properties emerge from interacting cerium ions, whose ground state doublet (with J = 5/2,m_J = ±3/2) arises from strong spin orbit coupling and crystal field effects. With the help of finite temperature Lanczos calculations, we determine the low energy effective spin-1/2 Hamiltonian parameters using which we reproduce all the prominent features of the dynamical spin structure factor. These parameters suggest the realization of a U(1) π-flux QSL phase [3] and they allow us to make predictions for responses in an applied magnetic field that highlight the important role played by octupoles in the disappearance of spectral weight.

*Supported by FSU and NHMFL, funded by NSF/DMR-1644779 and the State of Florida, and NSF DMR-2046570

[1] K. W. Plumb, H. J. Changlani, A. Scheie, S. Zhang, J. W. Krizan, J. A. Rodriguez-Rivera, Yiming Qiu, B. Winn, R. J. Cava & C. L. Broholm, Nature Physics 15, 54–59 (2019)
[2] S. Zhang, H. J. Changlani, K. W. Plumb, O. Tchernyshyov, and R. Moessner, Phys. Rev. Lett. 122, 167203 (2019)
[3] A.Bhardwaj, S.Zhang, H.Yan, R. Moessner, A. H. Nevidomskyy, H. J. Changlani, arXiv:2108.01096 (2021), under review.

Zoom Link: https://pitp.zoom.us/meeting/register/tJcqc-ihqzMvHdW-YBm7mYd_XP9Amhypv5vO