Arnab Adhikary, University of British Columbia
Novel Efficient regimes of computation in (finite) SPT chains
Spin chains exhibiting non-trivial symmetry protected topological (SPT) order are known to be perfect resources for measurement-based quantum computation. In a seminal work, Else et al. (2012) used group cohomological arguments to show that any 1D SPT chain is capable of shuttling quantum information without incurring any error. Unfortunately, the same analysis seemed to predict that performing any rotation away from the identity unavoidably introduces logical errors into the computation. Nevertheless, Miller and Miyake (2015) and Raussendorf et al. (2017) circumvented the roadblock by showing that logical decoherence can be efficiently managed in SPT ordered phases if the rotations are divided into smaller parts which are separated by a distance much larger than the characteristic length scale of the system. In this work, we investigate the exact opposite regime of computation, i.e. where the rotations are packed as closely as possible, and surprisingly find it to be the most resource efficient. The techniques developed in the process also make it feasible to test out our results in state of the art NISQ devices.
Anjishnu Bose, University of Toronto
Chiral Broken Symmetry Descendants of the Kagom\'e Lattice Chiral Spin Liquid
The breaking of chiral and time-reversal symmetries provides a pathway to exotic quantum phe- nomena and topological phases. Recent work has extensively explored the resulting emergence of chiral charge orders and chiral spin liquids on the kagom ́e lattice. Such chiral spin liquids are closely tied to bosonic fractional quantum Hall states with anyonic quasiparticles; however, their connection to nearby ordered states has remained a mystery. Here, we use spin-wave theory, parton Gutzwiller wavefunctions, and exact diagonalization, to show that two distinct magnetic orders with uniform scalar chirality – the XYZ umbrella state and the Octahedral spin crystal – emerge as competing orders in close proximity to the chiral spin liquid. Our work highlights the intimate link between a topologically ordered liquid and broken symmetry states with nontrivial real-space topology.
Matthew Duschenes, Perimeter Institute & University of Waterloo
Overparameterization of Realistic Quantum Systems
In order for quantum computing devices to accomplish preparation of quantum states, or simulation of quantum systems, exceptional control of experimental parameters is required. The optimal parameters, such as time dependent magnetic fields for nuclear magnetic resonance, are found via classical simulation and optimization. Such idealized parameterized quantum systems have been shown to exhibit different phases of training during optimization, such as overparameterization and lazy training, where global optima may potentially be reached exponentially quickly, while parameters negligibly change (Larocca et al., arXiv:2109.11676, 2021). Here, we study the effects of imposing constraints on the controls, such as bounding or sharing parameters across operators, and relevant noise channels are added after each time step. The constrained system is able to reach the overparameterized phase for certain noise models, however an order of magnitude more time steps are required. Compromises arise between numerical feasibility of exponential convergence, and experimental feasibility depending on the resolution of controls. This realistic approach offers insight into quantum control, learning in a quantum setting, and the ability of variational ansatz to account for noise.
SangEun Han, University of Toronto & Daniel Schultz, University of Toronto
Microscopic theory of multi-stage Fermi surface reconstruction in heavy fermion systems with quartet multipolar local moments
Recent experiments on \text{Ce}_{3}\text{Pd}_{20}\text{(Si,Ge)}_{6} show novel quantum critical behaviors associated with two consecutive quantum phase transitions upon varying the external magnetic field. Interestingly, the derivative of the Hall conductivity shows a discontinuous jump at each phase transition, which was attributed to sequential Fermi surface reconstructions. Motivated by this discovery and previous theory work, we consider a microscopic model of itinerant electrons coupled to the local moments described by a quartet of ground states in a crystal-electric-field (CEF). Such a quartet arises due to two degenerate Kramers doublets of \text{Ce}^{3+} ions in a cubic CEF and supports a large number of dipolar, quadrupolar, and octupolar moments. Specifically, we investigate emergent quantum phase transitions and criticality in a local effective model, the so-called Bose-Fermi Kondo model. This model describes the competition between the Kondo effect with the itinerant electrons and RKKY interaction for all of the 15 symmetry-allowed multipolar moments. Using renormalization group analyses, we demonstrate that a multitude of quantum phase transitions can occur depending on which multipolar moments participate in the Fermi surface formation and which other multipolar moments are decoupled via Kondo destruction. We provide a concrete example of two consecutive quantum phase transitions that involve the quadrupolar and dipolar/octupolar moments at two different stages. Our work provides an illuminating insight as to the importance of local symmetries in understanding multipolar Kondo lattice systems and an outlook for future directions.
Andrew Hardy, University of Toronto
Nematic phases and elastoresistivity from a multiorbital non-fermi liquid
We propose and study a two-orbital lattice extension of the Sachdev-Ye-Kitaev model in the large-N limit. The phase diagram of this model features a high temperature isotropic strange metal which undergoes a first-order thermal transition into a nematic insulator or a continuous thermal transition into nematic metal phase, separated by a tunable tricritical point. These phases arise from spontaneous partial orbital polarization of the multiorbital non-Fermi liquid. We explore the spectral and transport properties of this model, including the d.c. elastoresistivity, which exhibits a peak near the nematic transition, as well as the nonzero frequency elastoconductivity. Our work offers a useful perspective on nematic phases and transport in correlated multiorbital systems.
Daniel Huerga, University of British Columbia
Variational quantum simulation of valence-bond solids
Variational quantum algorithms (VQA), generically characterized by a feedback loop between a quantum device and a classical optimizer, are at the center of current research for their potentiality in providing first useful applications of noisy intermediate scale quantum (NISQ) devices in problems ranging from quantum simulation to machine learning. In particular, quantum simulation of frustrated quantum magnets offers a natural arena for benchmark and development of VQA, as they pose a challenge to state-of-the-art numerical techniques, while at the same time host a plethora of phases with implications for material design and quantum computation. Here, we present a VQA to simulate two-dimensional (2D) frustrated quantum magnets in the thermodynamic limit. Built upon a cluster-Gutzwiller ansatz, a parameterized quantum circuit provides the wave function of the cluster, while information of the infinite lattice is provided through a self-consistent mean-field embedding. We provide benchmark numerical simulations of the paradigmatic J1-J2 Heisenberg antiferromagnet and show that the mean-fields push the convergence of the algorithm within long-range ordered phases. A quantum paramagnetic valence-bond solid phase with plaquette ordering is accessed through a quantum phase transition, opening a promising route for quantum simulation of 2D valence bond solid phases with current superconducting circuit technology.
Julian May-Mann, University of Illinois at Urbana Champaign
Topological Geometry-Charge Responses in Three-Dimensional Insulators
Quantized responses are important tools for understanding and characterizing the universal features of topological phases of matter. Here, we consider a class of topological insulators in 3D with n-fold lattice rotation symmetry. These insulators realize quantized mixed geometry-charge responses, where line-like disclination defects of the lattice carry fractionally quantized electric polarization. When the surface of these insulators is gapped, disclinations of the surface carry a fractional charge that is half the minimal amount that can occur in purely 2D systems. These effects and other related phenomena, are captured by a 3D topological response term that couples the lattice curvature to the electromagnetic field strength.
Vedangi Pathak, University of British Columbia
Majorana zero modes in a magnetic and superconducting hybrid vortex
We propose and investigate a new platform for the realization of Majorana zero modes in a thin-film heterostructure composed of an easy-plane ferromagnet and a superconductor with spin-orbit coupling. The system can support an energetically favorable bound state comprising a magnetic vortex and a superconducting vortex. We show that a hybrid vortex thus created can host a robust zero-energy Majorana bound state at its core over a wide range of parameters, with its partner zero mode located at the boundary of a disk-shaped topological region. We identify a novel mechanism underlying the formation of the topological phase that, remarkably, relies on the orbital effect of the magnetization field and not on the usual Zeeman effect. The in-plane components of magnetization couple to electrons as a gauge potential with non-zero curl, thus creating an emergent magnetic field responsible for the gapped topologically non-trivial region surrounding the vortex core. Our construction allows the mobility of magnetic vortices to be imposed on the Majorana zero mode at the core of the superconducting vortex. In addition, the system shows a rich interplay between magnetism and superconductivity which might aid in developing future devices and technologies.
Shengqi Sang, Perimeter Institute
Ultrafast Entanglement Dynamics in Monitored Quantum Circuits
We study the non-equilibrium entanglement dynamics in (1+1)D weakly monitored quantum circuits. Due to projective measurements' non-local influence on wavefunctions, entanglement dynamics in monitored circuits is "faster" than that in the unitary ones in several ways. Specifically, we find that a pair of well-separated regions can build up nontrivial entanglement in a timescale that is sublinear in their distance; and originally local information can spread super-ballistically with time. We also discuss the relation between coding properties and local information's decay in monitored circuits.
Joseph Sullivan, University of British Columbia
Generalized Floquet Codes
We will discuss a connection between frustrated quantum Hamiltonians and quantum error correcting codes with dynamically generated logical qubits. More specifically, we will show how generalized (both in spatial and qudit dimension) Kitaev models give a natural recipe for encoding logical information in a sequence of toric code states. We will describe a prescription for creating stable defects in these models. Relatedly, this scheme allows for the preparation of states with more exotic topological order such as the double semion phase (or any Abelian twisted quantum double) using low weight measurements.
Joseph Tindall, Flatiron Institute
Quantum Physics in Connected Worlds
Theoretical research into many-body quantum systems has focused almost exclusively on regular structures which have a small, simple unit cell and where only a vanishingly small number of pairs of the constituents directly interact. Motivated by rapid advances in control over the pairwise interactions and geometries in many-body simulators, we determine the fate of many-body spin systems on more general, arbitrary graphs. When placing the minimum possible constraints on the underlying graph, we prove and observe how, with certainty in the thermodynamic limit, such systems behave like a single collective spin and exhibit no many-body physics. We thus understand the emergence of complex many-body physics as dependent on `exceptional', geometrically constrained structures such as the low-dimensional, regular ones found in nature. Within the space of highly connected graphs we identify hitherto unknown exceptions via their inhomogeneity and use state-of-the-art Matrix Product State algorithms to observe how complexity is heralded in these systems by a large degree of entanglement and highly non-uniform correlation functions. By bringing a graph-theoretic approach to the realm of many-body physics, our work paves the way for the discovery and exploitation of a whole class of geometries which can host uniquely complex phases of matter.
Tarun Tummuru, University of British Columbia
Twisted multilayer nodal superconductors
Twisted bilayers of nodal superconductors were recently proposed as a promising platform to host superconducting phases that spontaneously break time-reversal symmetry. Here we extend this analysis to twisted multilayers, focusing on two high-symmetry stackings with alternating and constant twist angles. In analogy to alternating-twist multilayer graphene, the former can be mapped to twisted bilayers with renormalized interlayer couplings, along with a remnant gapless monolayer when the number of layers L is odd. In contrast, the latter exhibits physics beyond twisted bilayers, including the occurrence of ‘magic angles’ characterized by cubic band crossings when L mod 4 = 3. Owing to their power-law divergent density of states, such multilayers are highly susceptible to secondary instabilities. Within a BCS mean-field theory, defined in the continuum and on a lattice, we find that both stackings host chiral topological superconductivity in extended regions of their phase diagrams.
Ye Weicheng, Perimeter Institute
UV/IR Mixing in Marginal Fermi Liquids
When Fermi surfaces (FSs) are subject to long-range interactions that are marginal in the renormalization-group sense, Landau Fermi liquids are destroyed, but only barely. With the interaction further screened by particle-hole excitations through one-loop quantum corrections, it has been believed that these marginal Fermi liquids (MFLs) are described by weakly coupled field theories at low energies. In this Poster, we point out a possibility in which higher-loop processes qualitatively change the picture through UV-IR mixing, in which the size of the FS enters as a relevant scale. The UV-IR mixing effect enhances the coupling at low energies, such that the basin of attraction for the weakly coupled fixed point of a (2+1)-dimensional MFL shrinks to a measure-zero set in the low-energy limit. This UV-IR mixing is caused by gapless virtual Cooper pairs that spread over the entire FS through marginal long-range interactions. Our finding signals a possible breakdown of the patch description for the MFL and questions the validity of using the MFL as the base theory in a controlled scheme for non-Fermi liquids that arise from relevant long-range interactions.
Ryohei Weil, University of British Columbia
Investigating computational phases of matter on NISQ devices
The paradigm of measurement-based quantum computation (MBQC) provides an ideal setting for the characterization of computational resources. Recent theoretical developments have strengthened the connection between string order and computational power, extending the prior classification of MBQC resource states based on symmetry-protected topological (SPT) phases to finite settings. We present progress on realizing these results in experiment, discussing techniques for carrying out MBQC for general SPT resource states on currently available noisy-intermediate scale quantum (NISQ) devices.
Rui Wen, University of British Columbia
Bulk-boundary correspondence for intrinsically-gapless SPTs from group cohomology
Recent studies on gapless SPT(gSPT) have revealed interesting relations between their topological edge modes and emergent anomalies. In this work we take a further step towards systematical construction of gSPT from cohomology data and establish a direct connection between emergent anomaly, group extension, and topological edge states for any internal symmetry group in any dimension. In 2 and higher dimensions the emergent anomaly can also be satisfied by anomalous symmetry enriched topological order, which we refer to as quotient-symmetry enriched topological order(QSET) that is sharply distinguished from non-anomalous SETs by an edge phase transition.
Emily Zhang, University of Toronto
Geometrical frustration versus Kitaev interactions in BaCo2(AsO4)2
Recently, Co-based honeycomb magnets have been proposed as promising candidate materials to host the Kitaev spin liquid state. One of the front-runners is BaCo2(AsO4)2 (BCAO), where it was suggested that the exchange processes between Co2+ ions via the surrounding edge-sharing oxygen octahedra could give rise to bond-dependent Kitaev interactions. In this work, we present and analyze comprehensive inelastic neutron scattering studies of BCAO with fields in the honeycomb plane. Combining the constraints from the magnon excitations in the high-field polarized state and the inelastic spin structure factor measured in zero magnetic field, we examine two leading theoretical models: the Kitaev-type JK\Gamma\Gamma' model and the XXZ-J1J3 model. We show that the existing experimental data can be consistently accounted for by the XXZ-J1J3 model but not by the JK\Gamma\Gamma' model, and we discuss the implications of these results for the realization of a spin liquid phase in BCAO and more generally for the realization of the Kitaev model in cobaltates.
