Condensed Matter

I will discuss our recent work on the use of autoregressive neural networks for many-body physics. In particular, I will discuss two approaches to represent quantum states using these models and their applications to the reconstruction of quantum states, the simulation of real-time dynamics of open quantum systems, and the approximation of ground states of many-body systems displaying long-range order, frustration, and topological order. Finally, I will discuss how annealing in these systems can be used for combinatorial optimization where we observe solutions to problems that are orders of magnitude more accurate than simulated and simulated quantum annealing.

While sharply-quantized topological features are conventionally associated with gapped phases of matter, there are a growing number of examples of gapless systems with topologically protected edge states. A particularly striking set of examples are "intrinsically gapless" symmetry-protected topological states (igSPTs), which host topological surface states that could not arise in a gapped system with the same symmetries. Examples include familiar non-interacting Weyl semimetals with Fermi arc surface states, as well as more exotic examples like deconfined quantum critical points with topological edge states. In this talk, I will discuss recent progress in formally understanding the bulk-boundary correspondence of strongly-interacting igSPTs using tools from group cohomology. In these examples, the gapless-ness of the bulk and presence of topological surface states can be understood in a unified way due to the presence of an emergent anomaly. Our formalism allows construction of lattice-models with such emergent anomalies whose topological properties can be deduced exactly.

Luttinger's theorem connects a basic microscopic property of a given metallic crystalline material, the number of electrons per unit cell, to the volume, enclosed by its Fermi surface, which defines its low-energy observable properties. Such statements are valuable since, in general, deducing a low-energy description from microscopics, which may perhaps be regarded as the main problem of condensed matter theory, is far from easy. In this talk I will present a unified framework, which allows one to discuss Luttinger theorems for ordinary metals, as well as closely analogous exact statements for topological (semi)metals, whose low-energy description contains either discrete point or continuous line nodes. This framework is based on the 't Hooft anomaly of the emergent charge conservation symmetry at each point on the Fermi surface, a concept recently proposed by Else, Thorngren and Senthil [Phys. Rev. X {\bf 11}, 021005 (2021)]. We find that the Fermi surface codimension $p$ plays a crucial role for the emergent anomaly. For odd $p$, such as ordinary metals ($p=1$) and magnetic Weyl semimetals ($p=3$), the emergent symmetry has a generalized chiral anomaly. For even $p$, such as graphene and nodal line semimetals (both with $p=2$), the emergent symmetry has a generalized parity anomaly. When restricted to microscopic symmetries, such as $U(1)$ and lattice symmetries, the emergent anomalies imply (generalized) Luttinger theorems, relating Fermi surface volume to various topological responses. The corresponding topological responses are the charge density for $p=1$, Hall conductivity for $p=3$, and polarization for $p=2$. As a by-product of our results, we clarify exactly what is anomalous about the surface states of nodal line semimetals.

The preparation of long-range entangled states using unitary circuits is limited by Lieb-Robinson bounds, but circuits with projective measurements and feedback (``adaptive circuits'') can evade such restrictions. We introduce three classes of local adaptive circuits that enable low-depth preparation of long-range entangled quantum matter characterized by gapped topological orders and conformal field theories (CFTs). The three classes are inspired by distinct physical insights, including tensor-network constructions, multiscale entanglement renormalization ansatz (MERA), and parton constructions. A large class of topological orders, including chiral topological order, can be prepared in constant depth or time, and one-dimensional CFT states and non-abelian topological orders with both solvable and non-solvable groups can be prepared in depth scaling logarithmically with system size. We also build on a recently discovered correspondence between symmetry-protected topological phases and long-range entanglement to derive efficient protocols for preparing symmetry-enriched topological order and arbitrary CSS (Calderbank-Shor-Steane) codes. Our work illustrates the practical and conceptual versatility of measurement for state preparation.

One of the central themes of condensed matter physics is the emergence of universality classes. In general, it is highly complex to determine which universality class emerges in a quantum matter based on its microscopic properties. In this talk, I will argue that the perspective of quantum anomaly provides powerful insights into the understanding of the landscape of universality classes that can emerge in a quantum matter, and I will present some interesting applications. Along the way, I will discuss the notions of entanglement-enabled symmetry-breaking orders, non-Lagrangian quantum criticality, quantum spin liquids beyond the usual parton description, etc.

Quantum dot arrays are an emerging system to synthesize controlled many-body quantum states for quantum simulation and computation. When cooled to a low temperature, each quantum dot acts as a site on which the number of half-integer spin particles can be controlled using voltages applied to gates, not unlike the gates on classical transistors. Moreover, the spin can be controlled and measured with the help of patterns of gates. It has recently been shown that tunnel couplings between individual sites can be controlled using the same gates to emulate a Hubbard model (unlike other systems i.e., superconductors, trapped ions, Rydberg atoms, etc), making it possible to program a many-body system using only voltages applied to gates, and that the spin can be initialized, controlled and read out on arrays of 4 to 6 quantum dots like a conventional quantum computer (unlike cold atoms in optical lattices). It has also recently been shown that the coherence times of the spin degree of freedom can be as long as 10 ms in this material system, and that the quantum dots can be proximized to superconductors. In this talk I will describe our efforts towards synthesis of interesting quantum states using this platform, at our lab in University of British Columbia.

We discuss emergent non-Fermi liquid behaviors in multipolar Kondo systems, where conduction electrons interact with the non-Kramers local moments carrying higher-rank multipolar moments such as quadrupolar and octupolar moments. We first show that unexpected non-Fermi liquid states arise in the single impurity multipolar Kondo system using the renormalization group and conformal field theory. Next, we study the competition between the Kondo and RKKY interactions in the Bose-Fermi Kondo systems, where the RKKY interaction between multipolar moments is represented by a bosonic degree of freedom. We present the renormalization group solution of this problem and describe the quantum critical behaviors. If time permits, we also discuss possible superconducting states arising from the multipolar Kondo interactions. We compare the theoretical results with existing experimental data on some cubic f-electron systems.

We develop a field-theoretic functional renormalization group formalism for field theories of metals that include all gapless modes around the Fermi surface. Due to the presence of intrinsic scales (Fermi momenta), the usual notion of scale invariance and renormalizable field theory need to be generalized. The formalism is applied to the non-Fermi liquid that arises at the anti-ferromagnetic quantum critical point in two space dimensions. We identify the interacting non-Fermi liquid fixed point in the space of coupling functions, and extract the universal scaling behaviour of the normal state and the pathway to the superconducting state at low energies.

3:15PM Arnab Adhikary 3:18PM Anjishnu Bose 3:21PM Matthew Duschenes 3:24PM SangEun Han & Daniel Schultz 3:27PM Andrew Hardy 3:30PM Daniel Huerga 3:33PM Vedangi Pathak 3:36PM Shengqi Sang 3:39PM Joseph Tindall 3:42PM Tarun Tummuru 3:45PM Ryohei Weil 3:48PM Rui Wen 3:51PM Ye Weicheng 3:54PM Emily Zhang

Unlike the half spin Kitaev honeycomb model which can be solved by an exact parton construction, the higher spin analogue of it is not solvable and it is still controversial if it exhibits a quantum spin liquid phase. In this talk, I will present a generalized parton construction where each spin-S is represented by 8S Majorana fermions. This framework naturally leads to a Z2 spin liquid when S is a half integer and gives a trivial ground state when S is an integer. Particularly, in the Z2 spin liquid, the Z2 charge is carried by a product of 2S Majorana fermions. In the anisotropic limit, say the interaction on the z bond is much stronger than others, the charges are gapped and the higher spin Kitaev model is reduced to a Wen-plaquette model exhibiting Z2 topological order. However, it is expected that at certain interaction strength on the x,y,z bond, the charges become gapless which results in a gapless Z2 spin liquid.

"Magnetic materials with 4d or 5d transition metals have drawn much attention for their unique magnetic properties arising from J_eff=1/2 magnetic states. Among them, a honeycomb lattice material with unusual bond-dependent interactions called Kitaev interactions is of particular interest due to the potential for realizing the Kitaev quantum spin liquid state. Although much progress has been made in understanding magnetic and spin-orbit excitations in Kitaev materials, such as Na2IrO3 and alpha-RuCl3, using resonant inelastic X-ray scattering (RIXS), there are still many unanswered questions regarding the nature of electronic excitations in these materials. Of particular interest is the sharp peak observed around 0.4 eV in the RIXS spectrum of Na2IrO3, the exact nature of which remains controversial. In this context, it is interesting to note that a similar lower energy “excitonic” peak was observed in our recent RIXS investigation of alpha-RuCl3. Given that the electronic parameters in alpha-RuCl3 are probably very different from those in Na2IrO3 (alpha-RuCl3 has a large bandgap of ~1eV, well above any SO excitation energy scale), the observed similarity is surprising. The RIXS spectra from these two compounds as well as other Kitaev materials will be compared and the origin of common spectral features will be discussed. "

"The relatively weak van der Waals bond in 2D materials has ushered in a rich new era of stacking engineering. We recently found in rhombohedrally stacked MoS2, a Berry phase contrast between layers can induce an asymmetric interlayer coupling and an out-of-plane spontaneous electrical polarization (1). The polarization direction can be switched via interlayer sliding, forming a new type of ferroelectricity. In addition, we demonstrated that such a polarization can lead to a spontaneous photovoltaic effect without any pn junctions (2). Compared to conventional PV effects, our device shows a similar quantum efficiency with an ultrafast speed and potentially a programmable polarity. The rhombohedrally stacked transition metal dichalcogenides therefore provide a new platform for studying spontaneous polarization at the atomic scale. (1) Jing Liang, et al, arXiv:2209.06966 (2022). (2) Dongyang Yang, et al, Nature Photonics, 16, 469–474 (2022)."