Format results
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Transport bounds: from resistor networks to quantum chaos
Andrew Lucas University of Colorado Boulder
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Entanglement and thermodynamics after a quantum quench in integrable systems
Vincenzo Alba SISSA International School for Advanced Studies
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Twist Fields in Quantum Field Theory: Entanglement Measures and Pentagonal Amplitudes
Olalla Alvaredo City, University of London
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Emergent hydrodynamics in integrable systems out of equilibrium
Benjamin Doyon King's College London
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The mother of all states of the kagome quantum antiferromagnet
Hitesh Changlani Johns Hopkins University
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Spectrum of conformal gauge theories on a torus
Alex Thomson California Institute of Technology
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Anomalous transport property in the nodal metallic spin ice Pr2Ir2O7
Akito Sakai University of Tokyo
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Driven Phases of Quantum Matter
Vedika Khemani Stanford University
Clean and interacting periodically driven quantum systems are believed to exhibit a single, trivial “infinite-temperature” Floquet-ergodic phase. By contrast, I will show that their disordered Floquet many-body localized counterparts can exhibit distinct ordered phases with spontaneously broken symmetries delineated by sharp transitions. Some of these are analogs of equilibrium states, while others are genuinely new to the Floquet setting. I will show that a subset of these novel phases are "time-crystals" in that they spontaneously break the underlying time-translation symmetry of the Floquet drive. Strikingly, the time-crystal phase is remarkably stable to all weak local deformations of the underlying Floquet drives, and the phase simultaneously also spontaneously breaks Hamiltonian dependent emergent spatial symmetries. Thus, the time-crystallinity goes hand in hand with spatial symmetry breaking and, altogether, these phases exhibit a novel form of simultaneous long-range order in space and time. I will describe how this spatiotemporal order can be detected in experiments involving quenches from a broad class of initial states.
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Transport bounds: from resistor networks to quantum chaos
Andrew Lucas University of Colorado Boulder
The Kovtun-Son-Starinets conjecture that the ratio of the viscosity to the entropy density was bounded from below by fundamental constants has inspired over a decade of conjectures about fundamental bounds on the hydrodynamic and transport coefficients of strongly interacting quantum systems. I will present two complementary and (relatively) rigorous approaches to proving bounds on the transport coefficients of strongly interacting systems. Firstly, I will discuss lower bounds on the conductivities (and thus, diffusion constants) of inhomogeneous fluids, based around the principle that transport minimizes the production of entropy. I will show explicitly how to use this principle in classical theories, and in theories with a holographic dual. Secondly, I will derive lower bounds on sound velocities and diffusion constants arising from the consistency of hydrodynamics with quantum decoherence and chaos, in large N theories. I will discuss the possible tension of such bounds with (some) holographic theories, and discuss resolutions to some existing puzzles.
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Entanglement and thermodynamics after a quantum quench in integrable systems
Vincenzo Alba SISSA International School for Advanced Studies
Entanglement and entropy are key concepts standing at the foundations of quantum and statistical mechanics, respectively. In the last decade the study of quantum quenches revealed that these two concepts are intricately intertwined. Although the unitary time evolution ensuing from a pure initial state maintains the system globally at zero entropy, at long time after the quench local properties are captured by an appropriate statistical ensemble with non zero thermodynamic entropy, which can be interpreted as the entanglement accumulated during the dynamics. Therefore, understanding the post-quench entanglement evolution unveils how thermodynamics emerges in isolated quantum systems. An exact computation of the entanglement dynamics has been provided only for non-interacting systems, and it was believed to be unfeasible for genuinely interacting models. Conversely, here we show that the standard quasiparticle picture of the entanglement evolution, complemented with integrability-based knowledge of the asymptotic state, leads to a complete analytical understanding of the entanglement dynamics in the space-time scaling limit. Our framework requires only knowledge about the steady state, and the velocities of the low-lying excitations around it. We provide a thorough check of our result focusing on the spin-1/2 Heisenberg XXZ chain, and considering quenches from several initial states. We compare our results with numerical simulations using both tDMRG and iTEBD, finding always perfect agreement.
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Twist Fields in Quantum Field Theory: Entanglement Measures and Pentagonal Amplitudes
Olalla Alvaredo City, University of London
Branch point twist fields play an important role in the study of measures of entanglement such as the Rényi entropies and the Negativity. In 1+1 dimensions such measures can be written in terms of multi-point functions of branch point twist fields. For 1+1-dimensional integrable quantum field theories and also in conformal field theory much is known about how to compute correlation functions and, with the help of the twist field, this knowledge can be exploited in order to gain new insights into the properties of various entanglement measures. In this talk I will review some of our main results in this context.
I will then go on to introduce a new (related) class of fields we have recently named conical twist fields. These are fields whose two-point functions have (surprisingly) been found to describe gluon amplitudes in the strong coupling limit of super Yang-Mills theories and therefore have featured in a completely different context from that of entanglement measures. Interestingly, at critical points, branch point and conical twist fields have the same conformal dimension and beyond criticality they also have very similar form factors, however they are different in many other respects. In my talk I will discuss and justify some of their similarities and differences.
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Dataset Augmentation in Feature Space - Graham Taylor
Dataset augmentation, the practice of applying a wide array of domain-specific transformations to synthetically expand a training set, is a standard tool in supervised learning. While effective in tasks such as visual recognition, the set of transformations must be carefully designed, implemented, and tested for every new domain, limiting its re-use and generality. In this talk, I will describe recent methods that transform data not in input space, but in a feature space found by unsupervised learning. We start with data points mapped to a learned feature space and apply simple transformations such as adding noise, interpolating, or extrapolating between them. Working in the space of context vectors generated by sequence-to-sequence recurrent neural networks, this simple and domain-agnostic technique is demonstrated to be effective for both static and sequential data.
Bio: Graham Taylor is an Associate Professor at the University of Guelph where he leads the Machine Learning Research Group. He is a member of the Vector Insitute for Artificial Intelligence and is an Azrieli Global Scholar with the Canadian Institute for Advanced Research. He received his PhD in Computer Science from the University of Toronto in 2009, where he was advised by Geoffrey Hinton and Sam Roweis. He spent two years as a postdoc at the Courant Institute of Mathematical Sciences, New York University working with Chris Bregler, Rob Fergus, and Yann LeCun.
Dr. Taylor's research focuses on statistical machine learning, with an emphasis on deep learning and sequential data. Much of his work has focused on "seeing people" in images and video, for example, activity and gesture recognition, pose estimation, emotion recognition, and biometrics.
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Emergent hydrodynamics in integrable systems out of equilibrium
Benjamin Doyon King's College London
The hydrodynamic approximation is an extremely powerful tool to describe the behavior of many-body systems such as gases. At the Euler scale (that is, when variations of densities and currents occur only on large space-time scales), the approximation is based on the idea of local thermodynamic equilibrium: locally, within fluid cells, the system is in a Galilean or relativistic boost of a Gibbs equilibrium state. This is expected to arise in conventional gases thanks to ergodicity and Gibbs thermalization, which in the quantum case is embodied by the eigenstate thermalization hypothesis. However, integrable systems are well known not to thermalize in the standard fashion. The presence of infinitely-many conservation laws preclude Gibbs thermalization, and instead generalized Gibbs ensembles emerge. In this talk I will introduce the associated theory of generalized hydrodynamics (GHD), which applies the hydrodynamic ideas to systems with infinitely-many conservation laws. It describes the dynamics from inhomogeneous states and in inhomogeneous force fields, and is valid both for quantum systems such as experimentally realized one-dimensional interacting Bose gases and quantum Heisenberg chains, and classical ones such as soliton gases and classical field theory. I will give an overview of what GHD is, how its main equations are derived, its relation to quantum and classical integrable systems, and some geometry that lies at its core. I will then explain how it reproduces the effects seen in the famous quantum Newton cradle experiment, and how it leads to exact results in transport problems such as Drude weights and non-equilibrium currents.
This is based on various collaborations with Alvise Bastianello, Olalla Castro Alvaredo, Jean-Sébastien Caux, Jérôme Dubail, Robert Konik, Herbert Spohn, Gerard Watts and my student Takato Yoshimura, and strongly inspired by previous collaborations with Denis Bernard, M. Joe Bhaseen, Andrew Lucas and Koenraad Schalm.
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The mother of all states of the kagome quantum antiferromagnet
Hitesh Changlani Johns Hopkins University
Frustrated magnets provide a fertile ground for discovering exotic states of matter, such as those with topologically non-trivial properties. Motivated by several near-ideal material realizations, we focus on aspects of the two-dimensional kagome antiferromagnet. I present two of our works in this area both involving the spin-1/2 XXZ antiferromagnetic Heisenberg model. First, guided by a previous field theoretical study, we explore the XY limit ($J_z=0$) for the case of 2/3 magnetization (i.e. 1/6 filling of hard-core bosons) and perform exact numerical computations to search for a "chiral spin liquid phase". We provide evidence for this phase by analyzing the energetics, determining minimally entangled states and the associated modular matrices, and evaluating the many-body Chern number [1]. The second part of the talk follows from an unexpected outcome of the first work, which realized the existence of an exactly solvable point for the ratio of Ising to transverse coupling $J_z/J=-1/2$. This point in the phase diagram has "three coloring" states as its exact ground states, exists for all magnetizations (fillings) and is found to be the source or "mother" of the observed phases of the kagome antiferromagnet. Using this viewpoint, I revisit certain aspects of the highly contentious Heisenberg case (in zero field) and suggest that it is possibly part of a line of critical points.
[1] K. Kumar, H. J. Changlani, B. K. Clark, E. Fradkin, Phys. Rev. B 94, 134410 (2016)
[2] H. J. Changlani, D. Kochkov, K. Kumar, B. K. Clark, E. Fradkin, under review. -
Spectrum of conformal gauge theories on a torus
Alex Thomson California Institute of Technology
Many model quantum spin systems have been proposed to realize critical points or phases described by 2+1 dimensional conformal gauge theories. On a torus of size L and modular parameter τ, the energy levels of such gauge theories equal (1/L) times universal functions of τ. We compute the universal spectrum of QED3, a U(1) gauge theory with Nf two-component massless Dirac fermions, in the large-Nf limit. We also allow for a Chern-Simons term at level k, and show how the topological k-fold ground state degeneracy in the absence of fermions transforms into the universal spectrum in the presence of fermions; these computations are performed at fixed Nf/k in the large-Nf limit.
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Numerical linked cluster spectroscopy of quantum spin ice
Numerical Linked Cluster (NLC) expansions can accurately compute thermal properties of quantum spin models in the thermodynamic limit in certain parameter regimes. In classical spin-ice models, where all correlations remain short-ranged down to T=0, these expansions can be convergent even at low T. However, for quantum spin-ice models, they converge only when either temperatures are not too small or there is a strong magnetic field present. To turn these studies into a spectroscopy of exchange parameters, when multiple exchange constants are relevant, is a challenge both because of the limited temperature-range of validity of effective spin-half models and difficulties in isolating magnetic properties in experiments at intermediate and high temperatures. We discuss ways in which such a spectroscopy can proceed. -
Anomalous transport property in the nodal metallic spin ice Pr2Ir2O7
Akito Sakai University of Tokyo
Pyrochlore Pr2Ir2O7 is a rare material with various unique properties such as geometrical frustration, c-f hybridization and Fermi node in the band structure. Although Pr3+ carries the effective moment of ~3B with Curie-Weiss temperature ~ 20 K, no long-range order is observed down to the partial freezing at Tf ~ 0.3 K, suggesting the geometrical frustration [1]. Magnetic Grüneisen ratio diverges mag ~ T-3/2 without tuning any parameter, indicating the zero-field quantum criticality [2]. Besides, recent angle-resolved photoemission spectroscopy (ARPES) measurement reveals the Fermi node at point in Pr2Ir2O7, which can be an origin of the various topological phases such as topological insulator and Weyl semimetal [3]. One of the most interesting and striking properties of Pr2Ir2O7 is non-trivial anomalous Hall effect: spontaneous Hall effect appears even in the absence of any spin freezing, which is attributed to the chiral spin liquid state [4]. In this presentation, we will discuss the recent results for the anomalous Hall effect for various samples of Pr2Ir2O7. -
Possible observation of photons and monopoles in the frustrated pyrochlore Yb2Ti2O7 and Pr2Zr2O7
Yuji Matsuda Kyoto University
We report highly unusual heat conduction generated by the spin degrees of freedom in spin liquid states of the pyrochlore magnets Yb2Ti2O7 and Pr2Zr2O7. In Yb2Ti2O7, the excitations propagate a long distance without being scattered, in contrast to the diffusive nature of classical monopoles. In Pr2Zr2O7, the thermal conductivity unexpectedly shows a dramatic enhancement at very low temperature. The low-lying excitations are discussed in terms of a possible emergent photons, coherent gapless spin excitations in a spin-ice manifold. -
The spectral periodicity of spinon continuum in quantum spin ice
Gang Chen Fudan University
Motivated by the rapid experimental progress of quantum spin ice materials, we study the dynamical properties of pyrochlore spin ice in the U(1) spin liquid phases. In particular, we focus on the spinon excitations that appear in high energies and show up as an excitation continuum in the dynamic spin structure factor. The keen connection between the crystal symmetry fractionalization of the spinons and the spectral periodicity of the spinon continuum is emphasized and explicitly demonstrated. The enhanced spectral periodicity of the spinon continuum provides a sharp physical observable to detect the spin quantum number fractionalization and U(1) spin liquid. Our prediction can be immediately examined by inelastic neutron scattering experiments among quantum spin ice materials with Kramers' doublets. Further application to the non-Kramers' doublets is discussed. If time permits, I will present some of our recent work in this field.