Quantum Matter

Unlike conventional global symmetries that act on all of space, subsystem symmetries act only on rigid subspaces such as lines, planes or fractal regions. Such symmetries are of interest for their close connection to fracton physics and in their own right. In this talk, I discuss phenomena that can occur in two-dimensional systems with subsystem symmetry and anyon excitations, where the symmetry fractionalizes on anyon excitations. This turns out to be manifest in the mobility of the fractionalized excitations under dynamics that respect the symmetry. Such symmetry fractionalization was previously thought to be impossible, and indeed there are a number of differences from conventional symmetry fractionalization. I will present a general framework to describe subsystem symmetry fractionalization in two dimensions, and give a number of simple examples of this phenomenon in commuting Pauli Hamiltonians.

This talk is based on arXiv:2203.13244, work in collaboration with David Stephen, Arpit Dua, José Garre-Rubio and Dominic Williamson.

Zoom Link: https://pitp.zoom.us/j/93741883840?pwd=RlMrUGwwVEt5WFdoNGpkMmdSVXp5UT09

We develop a new method for bosonizing the Fermi surface. In this method, a system with a Fermi surface is described as a coadjoint orbit of the group of canonical transformations. The method naturally parametrizes the Fermi surface by a bosonic field that depends on the spacetime coordinates and the position on the Fermi surface. The Wess-Zumino-Witten term in the effective action, governing the adiabatic phase acquired when the Fermi surface changes its shape, is completely fixed by the Kirillov-Kostant-Souriau symplectic form on the coadjoint orbit. We show that the resulting local effective field theory captures both linear and nonlinear effects in Landau’s Fermi liquid theory. Possible extensions of the theory are described.  Reference: arXiv:2203.05004.

Zoom Link: https://pitp.zoom.us/j/95453440138?pwd=b0Fmbi9HTU9nYTA3Y2F6dWlha294UT09

Magic-angle (θ=1.05∘) twisted bilayer graphene (MATBG) has shown two seemingly contradictory characters: the localization and quantum-dot-like behavior in STM experiments, and delocalization in transport experiments. We construct a model, which naturally captures the two aspects, from the Bistritzer-MacDonald (BM) model in a first principle spirit. A set of local flat-band orbitals (f) centered at the AA-stacking regions are responsible to the localization. A set of extended topological conduction bands (c), which are at small energetic separation from the local orbitals, are responsible to the delocalization and transport. The topological flat bands of the BM model appear as a result of the hybridization of f- and c-electrons. This model then provides a new perspective for the strong correlation physics, which is now described as strongly correlated f-electrons coupled to nearly free topological semimetallic c-electrons - we hence name our model as the topological heavy fermion model. Using this model, we obtain the U(4) and U(4)×U(4) symmetries as well as the correlated insulator phases and their energies. Simple rules for the ground states and their Chern numbers are derived. Moreover, features such as the large dispersion of the charge ±1 excitations and the minima of the charge gap at the Γ point can now, for the first time, be understood both qualitatively and quantitatively in a simple physical picture. Our mapping opens the prospect of using heavy-fermion physics machinery to the superconducting physics of MATBG. All the model’s parameters are analytically derived.

In recent years, generalizations of the notion of symmetry have significantly broadened our view on states of matter. We will discuss some recent progress of understanding and realizing the "fractal symmetry", where the symmetric charge i.e. the generator of the symmetry is defined on a fractal subset of the system with a noninteger or more generally irrational Hausdorff dimension. We will introduce a series of models with exotic fractal symmetries, which can in general be deduced from a "Pascal Triangle" (also called Yang Hui Triangle in ancient China) symmetry. We will discuss their various features including quantum phase transitions. We will also discuss the potential realization of these phases and phase transitions in experimental systems, such as the highly tunable platform of Rydberg atoms.

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Learning how to create, study, and manipulate highly entangled states of matter is key to understanding exotic phenomena in condensed matter and high energy physics, as well as to the development of useful quantum computers. In this talk, I will discuss recent experiments where we demonstrated the realization of a quantum spin liquid phase using Rydberg atoms on frustrated lattices and a new architecture based on the coherent transport of entangled atoms through a 2D array. Combining these results with novel technical tools on atom array platforms could open a broad range of possibilities for the exploration of entangled matter, with powerful applications in quantum simulation and information.

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Twisted interfaces between stacked van der Waals Cuprate crystals enable tunable Josephson coupling, utilizing anisotropic superconducting order parameters. Employing a novel cryogenic assembly technique, we fabricate high-temperature Josephson junctions with an atomically sharp twisted interface between Bi_2Sr_2CaCu_2O_{8+x} crystals. The critical current density J_c sensitively depends on the twist angle. While near 0 degree twist, J_c nearly matches that of intrinsic junctions, it is suppressed almost 2-orders of magnitude but remained finite near 45 degree. J_c also exhibits non-monotonic behavior versus temperature due to competition between two supercurrent contributions from nodal and anti-nodal regions of the Fermi surface. Near 45 degree twist angle, we observe two-period Fraunhofer interference patterns and fractional Shapiro steps at half integer values, a signature of co-tunneling Cooper pairs necessary for high temperature topological superconductivity.

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Recent advances in quantum simulation experiments have paved the way for a new perspective on strongly correlated quantum many-body systems. Digital as well as analog quantum simulation platforms are capable of preparing desired quantum states, and various experiments are starting to explore non-equilibrium many-body dynamics in previously inaccessible regimes in terms of system sizes and time scales. State-of-the art quantum simulators provide single-site resolved quantum projective measurements of the state. Depending on the platform, measurements in different local bases are possible. The question emerges which observables are best suited to study such quantum many-body systems.

In this talk, I will cover two different approaches to make the most use of these possibilities. In the first part, I will discuss the use of machine learning techniques to study the thermalization behavior of an interacting quantum system. A neural network is trained to distinguish non-equilibrium from thermal equilibrium data, and the network performance serves as a probe for the thermalization behavior of the system. We apply this method to numerically simulated data, as well experimental snapshots of ultracold atoms taken with a quantum gas microscope. 

In the second part of this talk, I will present a scheme to perform adaptive quantum state tomography using active learning. Based on an initial, small set of measurements, the active learning algorithm iteratively proposes the basis configurations which will yield the maximum information gain. We apply this scheme to GHZ states of a few qubits as well as ground states of one-dimensional lattice gauge theories and show an improvement in accuracy over random basis configurations.

Monitored quantum circuits (MRCs) exhibit a measurement-induced phase transition between area-law and volume-law entanglement scaling. In this talk, I will argue that MRCs with a conserved charge additionally exhibit two distinct volume-law entangled phases that cannot be characterized by equilibrium notions of symmetry-breaking or topological order, but rather by the non-equilibrium dynamics and steady-state distribution of charge fluctuations. These include a charge-fuzzy phase in which charge information is rapidly scrambled leading to slowly decaying spatial fluctuations of charge in the steady state, and a charge-sharp phase in which measurements collapse quantum fluctuations of charge without destroying the volume-law entanglement of neutral degrees of freedom. I will present some statistical mechanics and effective field theory approaches to such charge-sharpening transitions.

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We introduce a viewpoint that the Standard Model (SM) is a low-energy quantum vacuum arising from various neighbor Grand Unification (GUT) like vacua competition in an immense quantum phase diagram. In general, we find the SM arises near the gapless quantum critical regions between the competing neighbor vacua. Alternatively, we can also phrase this viewpoint in terms of the deformation class of quantum field theory (QFT), specified by its symmetry G and its anomaly (i.e., cobordism invariant). Seemly different QFTs of the same deformation class can be deformed to each other via quantum phase transitions. We show that GUT such as Georgi-Glashow su(5), Pati-Salam su(4)×su(2)×su(2), Barr’s flipped u(5), and familiar or modified so(n) models of Spin(n) gauge group, e.g., with n = 10, 18 can all reside in an appropriate SM deformation class, labeled by Z_{16} and Z_2 nonperturbative global anomaly index. We show that Ultra Unification, which replaces some of sterile neutrinos with new exotic gapped/gapless sectors (e.g., topological or conformal field theory) or gravitational sectors with topological origins via cobordism constraints, also resides in an SM deformation class. Neighbor quantum phases near SM or their phase transitions, and neighbor gauge enhanced gapless quantum criticality naturally exhibit beyond SM phenomena. We give a new proposal on the neutrino mass origin. The talk is mainly based on: arxiv 1910.14668, 2006.16996, 2008.06499, 2012.15860, 2106.16248, 2111.10369, 2112.14765. Some of these works are in collaboration with Zheyan Wan and Yi-Zhuang You. 

Zoom Link: https://pitp.zoom.us/j/94634619703?pwd=VWlWZHNIMm1sS2owWnlhSmhZTTNvUT09