Condensed Matter

To perform reliable quantum computations in the midst of noise from the environment, it is imperative to use a quantum error-correcting code — i.e., a scheme for redundantly encoding information so that errors may be detected and corrected as they occur. One of the most promising classes of quantum error-correcting codes are those based on topological phases of matter, such as the celebrated toric code. Although there is a rich classification of topological phases of matter, the toric code has by far received the most attention as a practical quantum error-correcting code, due to its simple representation within the stabilizer formalism.

In this talk, I will discuss three works in which we extend the stabilizer formalism to topological orders beyond that of the toric code. This includes the construction of two-dimensional stabilizer codes characterized by Abelian topological orders with gapped boundaries, three-dimensional stabilizer codes that host arbitrary two-dimensional Abelian topological orders on their surface, and two-dimensional subsystem codes also characterized by arbitrary Abelian topological orders. This work thus opens the door to encoding and processing quantum information using the exotic properties exhibited by the wide range of Abelian topological phases of matter.

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Zoom link https://pitp.zoom.us/j/94640905425?pwd=aDd0Qnl1TUU0QytaNWJJLzEyZlQrQT09

Frustrated quantum magnets provide a promising platform for realizing exotic phase transitions known as deconfined quantum critical points (DQCPs), where a conventional Landau-Ginzburg description fails and the resulting description involves emergent gauge fields. In the first part of my talk, I will propose a unified theory for describing a pair of continuous phase transitions numerically observed in the frustrated square lattice Heisenberg antiferromagnet, where a spin liquid phase appears to emerge in between Neel and valence bond solid (VBS) phases. The proposed DQCPs exhibit a plethora of unconventional phenomena, including anisotropic fixed points and dangerously irrelevant perturbations. In the second part of my talk, I will describe recent work analyzing an effective model of triangular lattice antiferromagnetism which supports coplanar magnetic order as well as VBS and spin liquid phases. We show that this effective model is sign-problem-free and amenable to large-scale Monte Carlo simulations, which reveal a direct transition between magnetic and VBS phases.

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Zoom link https://pitp.zoom.us/j/98562300020?pwd=OXYrL0dJTGkzNk5memlVM0tqY3hNQT09

We determine the low-energy spectrum and Parisi replica symmetry breaking function for the spin glass phase of the quantum Ising model with infinite-range random exchange interactions and transverse and longitudinal (h) fields. We show that, for all h, the spin glass state has full replica symmetry breaking, and the local spin spectrum is gapless with a spectral density which vanishes linearly with frequency. These results are obtained using an action functional - argued to yield exact results at low frequencies - that expands in powers of a spin glass order parameter, which is bilocal in time, and a matrix in replica space. We also present the exact solution of the infinite-range spherical quantum p-rotor model at nonzero h: here, the spin glass state has one-step replica symmetry breaking, and gaplessness only appears after imposition of an additional marginal stability condition.

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Zoom link https://pitp.zoom.us/j/98757418107?pwd=U1hiQnpKTDI4ajUyL04zRmQ4dVg3UT09

Driven by rapid advancements in quantum simulation capabilities across diverse physical platforms, open quantum systems are now of great interest, with special focus on thermalization processes of interacting many-body systems. Various techniques have been used to study operator spreading, to characterize entanglement dynamics, and even to identify exotic phases enabled by dynamical symmetries.

This talk will present a novel perspective on dynamical quantum systems that is capable of reproducing many previous results under a single intuitive framework and enables new results in symmetry-constrained systems. This is accomplished via a mapping between the dynamics averaged over Brownian random time evolution and the low-energy spectrum of a Lindblad superoperator, which acts as an effective Hamiltonian in a doubled Hilbert space. Doing so, we identify emergent hydrodynamics governing charge transport in open quantum systems with various symmetries, constraints, and ranges of interactions. By explicitly constructing dispersive excited states of this effective Hamiltonian using a single mode approximation, we provide a comprehensive understanding of diffusive, subdiffusive, and superdiffusive relaxation in many-body systems with conserved multipole moments and variable interaction ranges. Our approach further allows us to identify exotic Krylov-space-resolved diffusive relaxation despite the presence of dipole conservation, which we verify numerically. Therefore, we provide a simple, general, and versatile framework to qualitatively understand the dynamics of conserved operators under random unitary time evolution, and by extension, thermalizing quantum systems.

O. Ogunnaike, J. Feldmeier, J.Y. Lee, "Unifying Emergent Hydrodynamics and Lindbladian Low-Energy Spectra across Symmetries, Constraints, and Long-Range Interactions," arXiv:2304.13028 (accepted to PRL)

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It is well-known that one-dimensional systems at finite temperature, such as the classical Ising model, cannot spontaneously break a discrete symmetry due to the proliferation of domain walls. The validity of this statement rests on a few assumptions, including the spatial locality of interactions. In a situation where a one-dimensional system exists as a defect in a critical, higher-dimensional bulk system, the coupling between defect and bulk can induce an effective long-range interaction on the defect. It is thus natural to ask if long-range order can be stabilized on a defect in a critical bulk, which amounts to asking whether domain walls on the defect are relevant or not in the renormalization group sense. I will explore this question in the context of Ising conformal field theory in two and higher dimensions in the presence of a localized symmetry-breaking field. With both perturbative techniques and numerical conformal bootstrap, I will provide evidence that indeed the defect domain wall must be relevant when 2 < d < 4. For the bootstrap calculations, it is essential to include “endpoint” primary fields of the defect, which lead to a rigorous and powerful way to input bulk data. I will additionally give tight estimates of a number of other quantities, including  scaling dimensions of defect operators and the defect entropy, and I will conclude with a discussion of future directions.

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Zoom link https://pitp.zoom.us/j/92671628591?pwd=WjNma3VEV2M4T011dFlLMzM2ZUJiUT09

In this talk, we identify anomalies of 1+1d lattice Hamiltonian systems as ’t Hooft anomalies. We consider anomalies in internal symmetries as well as Lieb-Schultz-Mattis (LSM) type anomalies involving lattice translations. Using topological defects, we derive a simple formula for the ‘anomaly cocycle’ and show it is the obstruction to gauging even on the lattice. We reach this by introducing a systematic procedure to gauge arbitrary internal symmetries on the lattice that may not act on-site. As a by-product of our gauging procedure, we construct non-invertible lattice translation symmetries from LSM anomalies.

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Zoom link https://pitp.zoom.us/j/98084408560?pwd=cllSVnpWcEhPK21aVDZubU4yYWNyQT09

Anomaly of global symmetry is an important tool to study dynamics of quantum systems. In recent years, new non-invertible global symmetries are discovered in many quantum systems such as the 2d Ising model, Standard Model like theories, and lattice models. I will discuss constraints on the dynamics in 3+1d systems using anomalies of non-invertible symmetries from the perspective of bulk-boundary correspondence. The discussion is based on the work https://arxiv.org/abs/2308.11706 with Clay Cordova and Carolyn Zhang.

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Zoom link https://pitp.zoom.us/j/99162815973?pwd=M01nZXJIN2tCRjhuZlljNU1id01XQT09

I will introduce a new picture of quantum dynamics that might be thought of as "gauging" Schrodinger's picture that results in many "local" Hilbert spaces [1]. Truncating the dimensions of the local Hilbert spaces in this new picture yields an exciting new kind of tensor network whose computational cost does not increase with increasing spatial dimension (for fixed bond dimension) [2]. More detail: Although quantum dynamics are local for local Hamiltonians, the locality is not explicit in the Schrodinger picture since the wavefunction amplitudes do not obey a local equation of motion. In the first part of this talk, I will introduce a new picture of quantum dynamics—the gauge picture—which is similar to Schrodinger's picture, but with the feature that spatial locality is explicit in the equations of motion. In a sense, the gauge picture might be thought of as the result of "gauging" the global unitary symmetry of quantum dynamics into a local symmetry[1]. In the second part of the talk, I discuss a new kind of tensor network ansatz that is inspired from the gauge picture. In the gauge picture, different regions of space are associated with different Hilbert spaces, which are related by gauge connections. By relaxing the unitary constraint on the gauge connections, we can truncate the Hilbert space dimensions associated with different regions to obtain an approximate description of quantum dynamics. This truncated gauge picture, which we dub "quantum gauge network", is intriguingly similar to a classical lattice gauge theory coupled to a Higgs field (which are "local" wavefunctions in the gauge picture), but with non-unitary connections. In one spatial dimension, a quantum gauge network can be easily mapped to a matrix product density operator, and a matrix product state can be mapped to a quantum gauge network. Unlike tensor networks such as PEPS, quantum gauge networks boast the advantage that for fixed bond dimension, the computational cost does not increase with the number of spatial dimensions! Encoding fermionic wavefunctions is also remarkably straightforward. We provide a simple algorithm for approximately simulating quantum dynamics of bosonic or fermionic Hamiltonians in any spatial dimension. We compare the new quantum dynamics algorithm to exact methods for fermion systems in up to three spatial dimensions [2]. [1] The Gauge Picture of Quantum Dynamics. arXiv:2210.09314 [2] Quantum Gauge Networks: A New Kind of Tensor Network. arXiv:2210.12151

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Zoom link: https://pitp.zoom.us/j/94596192271?pwd=MytzNUx4ZEZEemkvcEEzbllWM1J6QT09

Fermi liquid theory is a cornerstone of condensed matter physics. I will show how to formulate Fermi liquid theory as an effective field theory. In this approach, the space of low-energy states of a Fermi liquid is identified with a coadjoint orbit of the group of canonical transformations. The method naturally leads to a nonlinear bosonized description of the Fermi liquid with nonlinear corrections fixed by the geometry of the Fermi surface. I will present that the resulting local effective field theory captures both linear and nonlinear effects in Landau’s Fermi liquid theory. The approach can be extended to encompass non-Fermi liquids, which correspond to strongly interacting fixed points obtained by deforming Fermi liquids with relevant interactions. I will also discuss how Berry curvature can be captured in the effective field theory approach.

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Zoom link: https://pitp.zoom.us/j/95381972217?pwd=Ni9iQ2hrUVNnWTJERDRmZk9GaW1jZz09

The presence of many competing classical ground states in frustrated magnets implies that quantum fluctuations may stabilize quantum spin liquids (QSL), which are characterized by fractionalized excitations and emergent gauge fields. A paradigmatic example is the U(1) Dirac spin liquid (DSL), which at low-energies is described by emergent quantum electrodynamics in 2+1 dimensions (QED3), a strongly interacting field theory with conformal symmetry. While the DSL is believed to be intrinsically stable, its robustness against various other couplings has been largely unexplored and is a timely question, also given recent experiments on triangular-lattice rare-earth oxides. In this talk, using complementary perturbation theory and scaling arguments as well as results from numerical DMRG simulations, I will show that a symmetry-allowed coupling between (classical) finite-wavevector lattice distortions and monopole operators of the U(1) Dirac spin liquid generally induces a spin-Peierls instability towards a (confining) valence-bond solid state. Away from the limit of static distortions, I will argue that the phonon energy gap establishes a parameter regime where the spin liquid is expected to be stable.

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Zoom link https://pitp.zoom.us/j/96764903405?pwd=Y0gyU3hGSC9va0hzWnZRZFBOVmRCZz09

An ongoing program of work in statistical physics and quantum dynamics is concerned with understanding the character of systems which follow an unconventional approach towards thermal equilibrium. In this talk, I will add to this story by introducing examples of simple 1D systems---both classical and quantum---which thermalize in very unusual ways. These examples have dynamics which is strictly local and translation-invariant, but in spite of this, they: a) can have very long thermalization times, with expectation values of local operators relaxing only over times exponential in the system size; and b) can thermalize only when they are placed in extremely large baths, with the required bath size growing exponentially (or even faster) in system size. Proofs of these results will be given using techniques from geometric group theory, a beautiful area of mathematics concerned with the complexity and geometry of infinite discrete groups. This talk will be based on a paper in preparation with Shankar Balasubramanian, Sarang Golaparakrishnan, and Alexey Khudorozhkov.

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Zoom link: https://pitp.zoom.us/j/99430001465?pwd=NENlS1M5UGc5UWM1ekQvRWFrZGYyUT09

Quantum Hall phases are the most exotic experimentally established quantum phases of matter.Recently they have been discovered at zero external magnetic field in two dimensional moire materials. I will describe recent work (with Xue-Yang Song and Ya-Hui Zhang) on their proximate phases and associated phase transitions that is motivated by the high tunability of thede moire systems. These phase transitions (and some of the proximate phases) are exotic as well, and realize novel ‘beyond Landau’ criticality that have been explored theoretically for many years. I will show that these moiré platforms provide a great experimental opportunity to study these unconventional phase transitions and related unconventional phases, thereby opening a new direction for research in quantum matter.

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Zoom link : https://pitp.zoom.us/j/97483204701?pwd=S2x4ck9tNHFjM0RiTDNWNFhaMk9SUT09