Condensed Matter

Fracton models are characterized by an exponentially increasing ground state degeneracy and point excitations with constrained motion. In this talk, I will focus on a prototypical 3D fracton model -- the X-cube model -- and discuss how its ground state degeneracy can be understood from a foliation structure in the model. In particular, we show that there are hidden 2D topological layers in the 3D bulk. To calculate the ground state degeneracy, we can remove the layers until a minimal structure is reached. The ground state degeneracy comes from the combination of the degeneracy of the foliation layers and that associated with the minimal structure. We discuss explicitly how this works for X-cube model with periodic boundary condition, open boundary condition, and even in the presence of screw dislocation defects.

Despite decades of theoretical work, the physical realization of topological order, outside of the fractional quantum Hall effect, has proved to be an elusive goal. Even the simplest example of a time-reversal symmetric topological order, as encountered in the paradigmatic toric code, awaits experimental realization. Key challenges include the lack of physically realistic models in these phases, and of ways to probe their defining properties. I will discuss a simple `Rydberg blockade' model, and describe numerical results that point to (i) a ground state with toric code topological order that could potentially be realized in experiment and (ii) ``smoking gun'' signatures of the phase which be accessed using a dynamic protocol. I will also briefly discuss how a topological qubit can be constructed in this platform by tuning boundaries as well as implications for constructing fault-tolerant quantum memories. Time permitting, a different platform for realizing exotic phases, magic-angle graphene and the special features of its band structure will be described, which make it a prime candidate for realizing fractional quantum Hall topological order even in the absence of a magnetic field.

References: arXiv:2011.12310. and arXiv:1912.09634
 

In this talk I will begin by introducing symmetry protected topological (SPT) Floquet systems in 1D. I will describe the topological invariants that characterize these systems,  and highlight their differences from SPT phases arising in static systems.  I will also discuss how the entanglement properties of a many-particle wavefunction depend on these  topological invariants. I will then show that the edge modes encountered in free fermion SPTs are remarkably robust to adding interactions, even in disorder-free systems where generic bulk quantities can heat to infinite temperatures due to the periodic driving. This robustness of the edge modes to heating can be understood in the language of strong modes for free fermion SPTs, and  almost strong modes for interacting SPTs.

I will then outline a tunneling calculation for extracting the long lifetimes of these edge modes by mapping the Heisenberg time-evolution of the edge operator to dynamics of a single particle in Krylov space. 

When the twist angle of a bilayer graphene is near the ``magic'' value, there are four narrow bands near the neutrality point, each two-fold spin degenerate. These bands are separated from the rest of the bands by energy gaps. In the first part of the talk, the topology of the narrow bands will be discussed, as well as the associated obstructions --or lack there of -- to construction of a complete localized basis [1,3].

In the second part of the talk, I will present a two stage renormalization group treatment [4] which connects the continuum Hamiltonian at length scales shorter than the moire superlattice period to the Hamiltonian for the active narrow bands only, which is valid at distances much longer than the moire period. Via a progressive numerical elimination of remote bands the relative strength of the one-particle-like dispersion and the interactions within the active narrow band Hamiltonian will be determined, thus quantifying the residual correlations and justifying the strong coupling approach in the final step.

In the last part of the talk, the states favored by electron-electron Coulomb interactions within the narrow bands will be discussed. Analytical and DMRG results based on 2D localized Wannier states [2,5], 1D localized hybrid Wannier states [3] and Bloch states [3,4] will be compared. Topological and symmetry constraints on the spectra of charged and neutral excitation[4] for various ground states, as well as non-Abelian braiding of Dirac nodes[3] , will also be presented.

[1] Jian Kang and Oskar Vafek, Phys. Rev. X 8, 031088 (2018).

[2] Jian Kang and Oskar Vafek, Phys. Rev. Lett. 122, 246401 (2019)

[3] Jian Kang and Oskar Vafek, Phys. Rev. B 102, 035161 (2020)

[4] Oskar Vafek and Jian Kang Phys. Rev. Lett. 125, 257602 (2020)

[5] Bin-Bin Chen, Yuan Da Liao, Ziyu Chen, Oskar Vafek, Jian Kang, Wei Li, Zi Yang Meng arXiv:2011.07602

In this talk I will present a general framework to distinguish different classes of charge insulators based on whether or not they insulate or conduct higher multipole moments (dipole, quadrupole, etc.). This formalism applies to generic many-body systems that support multipolar conservation laws. Applications of this work provide a key link between recently discovered higher order topological phases and fracton phases of matter.

We study the real-time dynamics of a small bubble of "false vacuum'' in a quantum spin chain near criticality, where the low-energy physics is described by a relativistic (1+1)-dimensional quantum field theory. Such a bubble can be thought of as a confined kink-antikink pair (a meson). We carefully construct bubbles so that particle production does not occur until the walls collide. To achieve this in the presence of strong correlations, we extend a Matrix Product State (MPS) ansatz for quasiparticle wavepackets [Van Damme et al., arXiv:1907.02474 (2019)] to the case of confined, topological quasiparticles. By choosing the wavepacket width and the bubble size appropriately, we avoid strong lattice effects and observe relativistic kink-antikink collisions. We use the MPS quasiparticle ansatz to identify scattering outcomes: In the Ising model, with transverse and longitudinal fields, we do not observe particle production despite nonintegrability (supporting recent numerical observations of nonthermalizing mesonic states). With additional interactions, we see production of confined and unconfined particle pairs. Although we simulated these low-energy, few-particle events with moderate resources, we observe significant growth of entanglement with energy and with the number of collisions, suggesting that increasing either will ultimately exhaust our methods. Quantum devices, in contrast, are not limited by entanglement production, and promise to allow us to go far beyond classical methods. We anticipate that kink-antikink scattering in 1+1 dimensions will be an instructive benchmark problem for relatively near-term quantum devices.

Recent years new concepts of symmetries have been developed such as higher form symmetries, and categorical symmetries. The higher form symmetries can be either explicit in a Hamiltonian, or inexplicit as a dual of an ordinary symmetry. The behavior of higher form symmetries are easy to evaluate in phases with gaps. But at quantum criticalities their behaviors are more nontrivial. We evaluate the behaviors of higher form symmetries (either explicit or inexplicit) at various quantum critical points, and demonstrate that for many quantum critical points a universal logarithmic contribution arises, which is analogous to the quantum entanglement entropy. This logarithmic contribution is related to the universal conductance at the quantum critical points, and in some cases can be computed exactly using duality between CFTs developed in last few years. We also evaluate the behavior of categorical symmetries for more exotic cases with subsystem symmetries.

The entanglement pattern of a quantum many-body system can be characterized by quasiparticles and emergent gauge fields, much like those found in Maxwell's theory. My talk begins with the basic aspects of symmetry fractionalization and emergent gauge fields in strongly correlated systems. I will further extend this paradigm into a new type of quantum many-body state, dubbed "fracton phase," from a quantum melting transition of plaquette paramagnetic crystals. These exotic states contain fractionalized sub-dimensional quasiparticles with constraint motion and emergent higher-rank gauge fields. Such constraint dynamics of the quasiparticles bring about an intriguing Bose metal phase with quasi-long range order and yields non-local quantum entanglement. In particular, the key peculiarities of this phase is the UV/IR mixing, where the short wavelength physics controls the low energy theory and hence challenges the standard notion of the renormalization group perspective.

Metals are ubiquitous in nature. One would like to determine the effective field theory that describe the low-energy physics of a metal. Many materials are successfully described by the so-called "Fermi liquid theory", but there is also much interest in "non-Fermi liquid metals" that evade such a description.

In this talk, I will present a very general perspective on metals that strongly constrains the possible effective field theories. The discussion is based on powerful theoretical concepts such as emergent symmetries and anomalies. From this perspective, combined with experimental observations, one can derive strong and unexpected conclusions about the nature of a particular kind of non-Fermi liquid metal, the "strange metal" observed in doped cuprates.

A many-body quantum system that is continually monitored by an external observer may be in distinct dynamical phases, depending on whether or not the observer’s repeated local measurements prevent the buildup of long-range entanglement. The universal properties of the “measurement phase transitions” between these phases remain a challenge. In this talk I will describe new theoretical approaches to measurement phase transitions, making connections with problems in statistical mechanics such as disordered magnets and travelling waves. I will show that exact results are possible in some regimes, including for quantum circuits with all-to-all interactions. (Based on arxiv:2009.11311)

Monitored quantum dynamics has attracted much research attention recently. Environmental monitoring typically leads to the decoherence of a quantum system. We explore the effect of energy-level decoherence in quench dynamics. In particular, we consider the linear quench across quantum critical phase transitions under the influence of decoherence. Due to the critical slowing down, the system will necessarily fall out of equilibrium in the vicinity of the critical point within a time scale known as the freeze-out time. The freeze-out time will scale with the quench rate following the Kibble-Zurek scaling. In the presence of decoherence, we found a new scaling behavior differed from the Kibble-Zurek scaling. We demonstrated our findings in the critical quench between 2D Chern insulator and trivial insulator. We show that the new scaling behavior can be justified from the behavior of Hall conductivity across the quantum quench.

Quantum circuits, relevant for quantum computing applications, present a new kind of many-body problem. Recently it was discovered that the quantum state evolved by random unitary gates, interrupted by occasional local measurements undergoes a phase transition from a highly entangled (volume law) state at small measurement rate to an area law state above a critical rate. I will review the current understanding of this transition from the statistical mechanics and the information perspectives. I will then argue that a circuit with intrinsic symmetries admits more phases, which represent distinct patterns of protection and flow of quantum information. These states can be studied and classified by mapping to an effective ground state problem of a Hamiltonian with enlarged effective symmetry. I will give two simple examples to illustrate these ideas: (i) a circuit with intrinsic Z2 spin symmetry; (ii) A circuit with Gaussian Majorana fermion gates showing a surprising Kosterlitz-Thouless transition in the entanglement content.