Condensed Matter

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

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.

The coupled wire construction is a powerful method for studying exotic quantum phases of matter. In this talk I will discuss some recent work in which this technique was used to realize new types of 3D compressible quantum phases. These phases possess a U(1) charge conservation symmetry that is weakly broken by rigid string or membrane-like order parameters. No local order parameter is present and the emergent quasiparticles have restricted mobility. I will discuss the unusual symmetry breaking mechanism and its connection to the compressibility. For a particular class of models I will also describe an effective low energy theory given by coupled layers Maxwell-Chern-Simons theories.

Zoom Link: https://pitp.zoom.us/j/95372524441?pwd=UTlVTTZlSmFRK0FmVE5pTHhDRThwdz09

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.