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 this mini course, I shall introduce the basic concepts in 2D topological orders by studying simple models of topological orders and then introduce topological quantum computing based on Fibonacci anyons. Here is the (not perfectly ordered) syllabus.                      

•        Overview of topological phases of matter
•        Z2 toric code model: the simplest model of 2D topological orders
•        Quick generalization to the quantum double model
•        Anyons, topological entanglement entropy, S and T matrices
•        Fusion and braiding of anyons: quantum dimensions, pentagon and hexagon identities
•        Fibonacci anyons
•        Topological quantum computing.

In this mini course, I shall introduce the basic concepts in 2D topological orders by studying simple models of topological orders and then introduce topological quantum computing based on Fibonacci anyons. Here is the (not perfectly ordered) syllabus.                      

•        Overview of topological phases of matter
•        Z2 toric code model: the simplest model of 2D topological orders
•        Quick generalization to the quantum double model
•        Anyons, topological entanglement entropy, S and T matrices
•        Fusion and braiding of anyons: quantum dimensions, pentagon and hexagon identities
•        Fibonacci anyons
•        Topological quantum computing.

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

This talk is motivated by the question: why do we put so much effort and investment into quantum computing? A short answer is that we expect quantum advantages for practical problems. To achieve this goal, it is essential to reexamine existing experiments and propose new protocols for future quantum advantage experiments. In 2019, Google published a paper in Nature claiming to have achieved quantum computational advantage, also known as quantum supremacy. In this talk, I will explain how they arrived at their claim and its implications. I will also discuss recent theoretical and numerical developments that challenge this claim and reveal fundamental limitations in their approach. Due to these new developments, it is imperative to design the next generation of experiments. I will briefly mention three potential approaches: efficient verifiable quantum advantage, hardware-efficient fault-tolerance, and quantum algorithms on analog devices, including machine learning and combinatorial optimization.

Zoom Link: https://pitp.zoom.us/j/96945612624?pwd=ckRKMFJqZ0Q0dGtFOU91c1hnMzIzZz09

Recent advances in programmable quantum devices brought to the fore the intriguing possibility of using them to realize and investigate topological quantum spin liquids (QSLs) phase. This new and exciting direction brings about important research questions on how to probe and determine the presence of such exotic, highly entangled phases. In this talk, I will discuss how to construct Z2 QSLs states as the ground state of a static Hamiltonian with only local two-qubit interactions and a transverse field, and demonstrate its realization in the classical limit at the endpoint of quantum annealing protocol, using D-Wave DW-2000Q machine . I will also demonstrate how to probe signatures of Z2 QSLs fractional statistics in quantum simulators via quasiparticle interferometry. At the end, I will show the robustness of this probe against disorders and dephasing -- effects that are generally pervasive in quantum devices nowadays.

Zoom Link: https://pitp.zoom.us/j/99207971920?pwd=N3R3YUJtWXJWVjFQWlRoZ3hYSDlMZz09

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