Condensed Matter

Macroscopic physics of a quantum many-body systems on a lattice is commonly captured by a continuum field theory. We will discuss the interplay between lattice effects and continuum theory from the perspective of symmetry and ’t Hooft anomalies. In the first part of the talk, using the example of a spin-1/2 XXZ chain, we will show how the continuum limit of a lattice model is properly described in terms of a field theory with topological defects. In particular, anomaly explains a curious size dependence of the ground state momentum in the XXZ chain. In the second part, we will examine U(1) filling anomaly for subsystem symmetries. With a generalized flux-insertion argument, we derive nontrivial constraints on the mobility of excitations in a symmetry-preserving gapped phase.

Zoom link:  https://pitp.zoom.us/j/96117447396?pwd=QVNaSHdHeDh1RENvenRjamVlVGNudz09

Fermi liquids are gapless quantum many-body states of fermions, which describes electrons in the normal state of most metals at low temperature. Despite its long history of study, there has been renewed interest in understanding the stability of Fermi liquid from the perspectives of emergent symmetry and quantum anomaly. In this talk, I will introduce the concept of Fermi surface anomaly and propose a possible scheme to classify it. The classification scheme is based on viewing the Fermi surface as the boundary of a Chern insulator in the phase space, with an unusual dimension counting arising from the non-commutative phase space geometry. This enables us to extend the notion of Fermi surface anomaly to the non-perturbative cases and discuss symmetric mass generation on the Fermi surface when the anomaly is canceled. I will provide examples of lattice models that demonstrate Fermi surface symmetric mass generation and make connections to the recent progress in understanding the pseudo-gap transition in cuprate materials.

Zoom link: https://pitp.zoom.us/j/97223165997?pwd=SkhJZEt1ejhQRm0yK2tKS3NhM2o2Zz09

Soon after the discovery of high temperature superconductivity in the cuprates, Anderson proposed a connection to quantum spin liquids. But observations since then have shown that the low temperature phase diagram is dominated by conventional states, with a competition between superconductivity and charge-ordered states which break translational symmetry. We employ the "pseudogap metal" phase, found at intermediate temperatures and low hole doping, as the parent to the phases found at lower temperatures. The pseudogap metal is described as a fractionalized phase of a single-band model, with small pocket Fermi surfaces of electron-like quasiparticles whose enclosed area is not equal to the free electron value, and an underlying pi-flux spin liquid with an emergent SU(2) gauge field. This pi-flux spin liquid is now known to be unstable to confinement at sufficiently low energies. We develop a theory of the different routes to confinement of the pi-flux spin liquid, and show that d-wave superconductivity, antiferromagnetism, and charge order are natural outcomes. We are argue that this theory provides routes to resolving a number of open puzzles on the cuprate phase diagram.

As a side result, at half-filling, we propose a deconfined quantum critical point between an antiferromagnet and a d-wave superconductor described by a conformal gauge theory of 2 flavors of massless Dirac fermions and 2 flavors of complex scalars coupled as fundamentals to a SU(2) gauge field.

This talk is based on Maine Christos, Zhu-Xi Luo, Henry Shackleton, Ya-Hui Zhang, Mathias S. Scheurer, and S. S., arXiv:2302.07885

Zoom link:  https://pitp.zoom.us/j/97370076705?pwd=Q1MwQmNaSFkxaWFEdUl5NFZDS0E4Zz09

The Berry phase, discovered by M.V. Berry in 1984, has been applied to the construction of various invariants in topological phase of matters. The Berry phase measures the non-triviality of a uniquely gapped system as a family and takes its value in $H^2({parameter space};Z)$.

In recent years, there have been several attempts to generalize it to higher-dimensional many-body lattice systems[1,2,3,4], called the “higher” Berry phase. In the case of spatial dimension d it is believed that the higher Berry phase takes its value in $H^{d+2}({parameter space};Z)$. However, in general dimensions, the definition of the higher Berry phase in lattice systems is not yet known.

In my talk, I’ll explain about the way to extract the higher Berry phase in 1-dimensional systems by using the “higher inner product” of three matrix product states and how to construct the topological invariant which takes its value in $H^3({parameter space};Z)$. This talk is based on [3] and [4].

Refs:
[1] A. Kapustin and L. Spodyneiko Phys. Rev. B 101, 235130
[2] X. Wen, M. Qi, A. Beaudry, J. Moreno, M. J. Pflaum, D. Spiegel, A. Vishwanath and M. Hermele arXiv:2112.07748
[3] S. Ohyama, Y. Terashima and  K. Shiozaki arXiv:2303.04252
[4] S. Ohyama and S. Ryu arXiv:2304.05356  

Zoom link:  https://pitp.zoom.us/j/93720709850?pwd=RTliMDNMRWo2V2k1MnBKUjlRMjBqZz09

In an isolated quantum many-body system undergoing unitary evolution, the entropy of a subsystem (smaller than half the system size) thermalizes if at long times, it is to leading order equal to the thermodynamic entropy of the subsystem at the same energy. We prove entropy thermalization for a nearly integrable Sachdev-Ye-Kitaev model initialized in a pure product state. The model is obtained by adding random all-to-all 4-body interactions as a perturbation to a random free-fermion model. In this model, there is a regime of “thermalization without eigenstate thermalization.” Thus, the eigenstate thermalization hypothesis is not a necessary condition for thermalization. Joint work with Aram W. Harrow

Zoom Link: https://pitp.zoom.us/j/91710478120?pwd=OVRDOStOSkdIVG9mcGJqMWJlU1FRdz09

Isolated quantum systems, investigated a century ago, exhibit coherent, unitary dynamics. When such a system is coupled to an environment, the resulting loss of coherence is modeled by completely positive, trace preserving (CPTP) quantum maps for the density matrix. A lossy atom, when it has not decayed, exhibits a coherent dynamics that is in a distinct, new class. Non-Hermitian Hamiltonians with parity-time symmetry govern this class and exhibit exceptional-point (EP) degeneracies with topological features. After a historical introduction to PT symmetry, I will present examples of coherent, quantum dynamics in the static and Floquet regimes for such systems with a superconducting transmon (Nature Phys. 15, 1232 (2019)), ultracold atoms (Nature Comm. 10, 855 (2019)), and integrated quantum photonics (Phys. Rev. Res. 4, 013051 (2022); Nature 557, 660 (2018)) as platforms. These include topological quantum state transfer, entanglement/coherence control, and super-quantum correlations. I will conclude with speculations on applicability of these ideas to quantum matter, particle physics, and strong gravity. 

(* with Anthony Laing group, Kater Murch group, Le Luo group, Sourin Das group).

Zoom link:  https://pitp.zoom.us/j/92391441075?pwd=QmRYSnYveUZCci9QZFcwUHBFS29QZz09

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