Quantum Matter

In this talk I will describe a topological response theory that predicts the physical manifestation of a class of topological invariants in systems with crystalline symmetry. I focus on two such invariants, the 'discrete shift' and a quantized charge polarization. Guided by theory, I discuss how these invariants can be extracted from lattice models by measuring the fractional charge at lattice disclinations and dislocations, as well as from the angular and linear momentum of magnetic flux. These methods are illustrated using the Hofstadter model of spinless fermions in a background magnetic field; they give new topological invariants in this model for the first time since the quantized Hall conductance was computed by TKNN in 1982.

Zoom link:  https://pitp.zoom.us/j/93633131128?pwd=d2h4U1l0ZVU5aE1ORURkdFNSanB4dz09

Periodic driving is a ubiquitous tool for controlling experimental quantum systems. When the drive fields are of comparable, incommensurate frequencies, new theoretical tools are required to treat the resulting quasiperiodic time dependence. Similarly, new and surprising phenomena of topological origin may emerge in this regime, including the quantized pumping of energy from one drive field to another. I will describe how to exploit this energy pumping to coherently translate––or boost––quantum states of a cavity in the Fock basis. This protocol enables the preparation of highly excited Fock states for use in quantum metrology––one need only boost low occupation Fock states. Energy pumping, and hence boosting, may be achieved nonadiabatically as a robust edge effect associated to a topological phase. I will present a simple coupled-layer model for the phase, and briefly describe the topological classification which characterizes its robust properties.

Zoom link:  https://pitp.zoom.us/j/94040881668?pwd=THh1WlIxZmZnYlp6QVRKRDhMWnk1UT09

It has long been known that the quantum ground state of a metal is characterized by an abstract manifold in the momentum space called the Fermi sea. Fermi sea can be distinguished topologically in much the same way that a ball can be distinguished from a donut by counting the number of holes. The associated topological invariant, i.e. the Euler characteristic (χ_F), serves to classify metals. Here I will survey two recent proposals relating χ_F  to experimental observables, namely: (i) equal-time density/number correlations, and (ii) Andreev state transport along a planar Josephson junction. Moreover, from the perspective of quantum information, I will explain how multipartite entanglement in real space probes the Fermi sea topology in momentum space. Our works not only suggest a new connection between topology and entanglement in gapless quantum matters, but also suggest accessible experimental platforms to extract the topology in metals. 

Zoom link:  https://pitp.zoom.us/j/98944473905?pwd=ak5nVmd4N0pSdXpjOFM0YnFJdnJ4dz09

Symmetry-protected topological (SPT) phases are short-range entanglement (SRE) quantum states which cannot be adiabatically connected to trivial product states in the presence of symmetries. Recently, it is shown that symmetry-protected short-range entanglement can still prevail even if part of the protecting symmetry is broken by quenched disorder locally but restored upon disorder averaging, dubbed as the average symmetry-protected topological (ASPT) phases. In this talk, I will systematically construct the ASPT phases as a mixed ensemble or density matrix, which may not be realized in a clean system without any disorder. I will also design the strange correlator of the ASPT phases via a strange density matrix to detect the nontrivial ASPT state. Moreover, it is amazing that the strange correlator of ASPT can be precisely mapped to the loop correlation functions of some proper statistical loop models, with power-law behaviors.

Zoom link:  https://pitp.zoom.us/j/91672345456?pwd=N0dNQXNmVVoybnNxYXJuWnVRME8rUT09

I will talk about the generalization of Berry classes for quantum lattice spin systems. It defines invariants of topologically ordered states or families thereof. In particular, its equivariant version for 2d gapped states gives the zero-temperature Hall conductance and its various generalizations. I will also discuss the construction of chiral states realizing the topological order associated with a unitary rational vertex operator algebra for which these invariants are non-trivial

Zoom link:  https://pitp.zoom.us/j/99910103969?pwd=VlVHVGRiV29iVEFyTXZyR3ovMkRaQT09

The multipartite entanglement structure for the ground states of two dimensional topological phases is an interesting albeit not well understood question. Utilizing the bulk-boundary correspondence, the tripartite entanglement calculation of 2d topological phases can be reduced to that on the vertex state, defined by the boundary conditions at the interfaces between spatial regions. In this work, we use the conformal interface technique to calculate the entanglement measures of the vertex state, which include the area-law, geometrical and topological pieces, and the possible extra order one contribution. This explains our previous observation of Markov gap h=\frac{c}{3}\ln 2 in the 3-vertex state, and generalizes it to the p-vertex state as well as rational conformal field theory, and more general choices of subsystem. Finally, we support our prediction by numerical evidence. 

Zoom link:  https://pitp.zoom.us/j/93914854044?pwd=eWl3eGVLU25XUGhKbnFRSm5ab0JuUT09

We construct an exactly solvable lattice model for a deconfined quantum critical point (DQCP) in (1+1) dimensions. This DQCP occurs in an unusual setting, namely at the edge of a (2+1) dimensional bosonic symmetry protected topological phase (SPT) with ℤ2×ℤ2 symmetry. The DQCP describes a transition between two gapped edges that break different ℤ2 subgroups of the full ℤ2×ℤ2 symmetry. Our construction is based on an exact mapping between the SPT edge theory and a ℤ4 spin chain. This mapping reveals that DQCPs in this system are directly related to ordinary ℤ4 symmetry breaking critical points. Based on arXiv:2206.01222.

Zoom link:  https://pitp.zoom.us/j/93794543360?pwd=Y3lidGZhRFNrUjEyMVpaNEgwTnE3QT09

The Floquet code implements a periodic sequence of two-qubit measurements to realize the topological order. After each measurement round, the instantaneous stabilizer group can be mapped to a honeycomb toric code, thus explaining the topological feature. However, the code also possesses a time-crystal order distinct from a stationary toric code – an e-m exchange after every cycle. In this work, we construct a continuous path interpolating between the Floquet and toric codes, focusing on the transition between the time-crystal and non-time crystal phases. We show that this transition is characterized by a diverging length scale. We also add single qubit noise to the model and obtain a two-dimensional parametric phase diagram of the Floquet code.

Zoom link:  https://pitp.zoom.us/j/95933569447?pwd=UkcrVHdkWERTNVIrcXdCREQ3Y1JUZz09

In this talk, I will introduce the so-called entanglement linear response, i.e., response under entanglement generated unitary dynamics. As an application, I will show how it can be applied to certain anomalies in 1D CFTs. Moreover, I will apply it to extract the quantum Hall conductance from a wavefunction and how it embraces a previous work on the chiral central charge. This gives a new connection between entanglement, anomaly and topological response. If time permits, I will also talk about how it inspires some generalizations of the real-space Chern number formula in free fermion systems.

Zoom link:  https://pitp.zoom.us/j/96535214681?pwd=MldXRkRjZ1J6WS95WXQ0cG03cWdCZz09

Many topological phases of lattice systems display quantized responses to lattice defects. Notably, 2D insulators with C_n lattice rotation symmetry hosts a response where disclination defects bind fractional charge. In this talk, I will show that the underlying physics of the disclination-charge response can be understood via a theory of continuum fermions with an enlarged SO(2) rotation symmetry. This interpretation maps the response of lattice fermions to disclinations onto the response of continuum fermions to spatial curvature. Additionally, in 3D, the response of continuum fermions to spatial curvature predicts a new type of lattice response where disclination lines host a quantized polarization. This disclination-polarization response defines a new class of topological crystalline insulator that can be realized in lattice models. In total, these results show that continuum theories with spatial curvature provide novel insights into the universal features of topological lattice systems. In total, these results show that theories with spatial curvature provide novel insights into the universal features of topological lattice systems.

Zoom link:  https://pitp.zoom.us/j/97325013281?pwd=MU5tdFYzTFljMGdaelZtNjJqbmRPZz09

In non-relativistic systems, the Lieb-Robinson Theorem imposes an emergent speed limit (independent of the relativistic limit set by c), establishing locality under unitary quantum dynamics and constraining the time needed to perform useful quantum tasks. We have extended the Lieb-Robinson Theorem to quantum dynamics with measurements. In contrast to the general expectation that measurements can arbitrarily violate spatial locality, we find at most an (M+1)-fold enhancement to the speed of quantum information, provided the outcomes of M local measurements are known; this holds even when classical communication is instantaneous. Our bound is asymptotically optimal, and saturated by existing measurement-based protocols (the "quantum repeater").  Our bound tightly constrain the resource requirements for quantum computation, error correction, teleportation, generating entangled resource states (Bell, GHZ, W, and spin-squeezed states), and preparing SPT states from short-range entangled states.

Zoom Link: https://pitp.zoom.us/j/95640053536?pwd=Z05oWlFRSEFTZWFRK2dwcHdsWlBBdz09

In this talk I will explore perspectives of quantum entanglement in (1+1)-d systems in presence of defects. The talk consists of two parts. In the first part, I will talk about the ground state entanglement entropy for 1d quantum spin chains with defects, using the transverse field Ising model and the three-state Potts model as examples. In the second part, I will describe the field theoretical replica trick approach to study entanglement entropy in such systems. This talk consists of some reviews about existing work, as well as work in progress with Linnea Grans-Samuelsson, Ananda Roy, Hubert Saleur, and Yifan Wang.

Zoom link: https://pitp.zoom.us/j/93049110080?pwd=QmpneGs2QlpZMlBROUlvU3VzaGtsZz09