Search results in Condensed Matter from PIRSA
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Kitaev spin liquids in spin-orbit coupled correlated materials
Hae-Young Kee University of Toronto
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Field-driven spin liquids in Kitaev materials
Simon Trebst Universität zu Köln
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Quantum Many-Body Scars and Space-Time Crystalline Order from Magnon Condensation
Tom Iadecola University of Maryland, College Park
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Phase transition of fractional Chern insulators: QED3 and beyond
Yin-Chen He Perimeter Institute for Theoretical Physics
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Application of Tensor Network States to Lattice Field Theories
Stefan Kuhn Deutsches Elektronen-Synchrotron DESY
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Dynamics of two-point correlation functions in quantum systems
Alvaro Alhambra Universidad Autonoma de Madrid
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Extracting conformal and superconformal data from critical quantum spin chains
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Ashley Milsted California Institute of Technology
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Yijian Zou Perimeter Institute for Theoretical Physics
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Topological phases in Kitaev Materials
Yong-Baek Kim University of Toronto
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Finite Correlation Length Scaling in Lorentz-Invariant Gapless iPEPS Wave Functions
Andreas Lauchli Paul Scherrer Institute
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Shortcuts in Real and Imaginary Time
Timothy Hsieh Perimeter Institute for Theoretical Physics
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Isometric Tensor Network States in Two Dimensions
Michael Zaletel University of California, Berkeley
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The "Zero Mode" in Kac Table: Revisiting the Ramond Sector of N=1 Superconformal Minimal Models
Chun Chen University of Alberta
We discover an infinite hierarchical web of the products of supersymmetric generators sustained by the superconformal Virasoro algebra. This hierarchy structure forms the mathematical foundation underpinning the explicit derivation of the character for the self-symmetric Ramond highest weight $c/24$. To consistently fit these exact results into the modular-invariant torus partition function, we advocate a necessary augmentation of the representation theory in the original Friedan--Qiu--Shenker construction via symmetrizing the ground-state manifold associated with the $c/24$ Verma module. Under the newly-proposed scheme, we invoke a quantum-interference mechanism between the two independent Ishibashi states to construct the boundary Cardy states for the whole family of the $\mathcal{N}=1$ superconformal minimal series, based on which the extra fusion channels are unveiled through the obtained Verlinde formula. Our work thus provides the first complete solution to this thirty-year-old question.
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Kitaev spin liquids in spin-orbit coupled correlated materials
Hae-Young Kee University of Toronto
Recently, a new family of correlated honeycomb materials with strong spin-orbit coupling have been promising candidates to realize the Kitaev spin liquid. In particular, a half-integer quantized thermal Hall conductivity was reported in alpha-RuCl3 under the magnetic field. Using a generic nearest neighbour spin model with bond-dependent interactions, I will present numerical evidence of an extended regime of quantum spin liquids. I will also discuss how to achieve a chiral spin liquid near ferromagnetic Kitaev interaction in the presence of the magnetic field leading to the quantized thermal Hall conductivity.
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Field-driven spin liquids in Kitaev materials
Simon Trebst Universität zu Köln
Kitaev materials — spin-orbit assisted Mott insulators, in which local, spin-orbit entangled j=1/2 moments form that are subject to strong bond-directional interactions — have attracted broad interest for their potential to realize spin liquids. Experimentally, a number of 4d and 5d systems have been widely studied including the honeycomb materials Na2IrO3, α-Li2IrO3, and RuCl3 as candidate spin liquid compounds — however, all of these materials magnetically order at sufficiently low temperatures. In this talk, I will discuss the physics of Kitaev materials that plays out when applying magnetic fields. Experiments on RuCl3 indicate the formation of a chiral spin liquid that gives rise to an observed quantized thermal Hall effect. Conceptually, this asks for a deeper understanding of the physics of the Kitaev model in tilted magnetic fields. I will report on our recent numerical studies that give strong evidence for a Higgs transition from the well known Z2 topological spin liquid to a gapless U(1) spin liquid with a spinon Fermi surface and put this into perspective of experimental studies.
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Quantum Many-Body Scars and Space-Time Crystalline Order from Magnon Condensation
Tom Iadecola University of Maryland, College Park
We study the eigenstate properties of a nonintegrable spin chain that was recently realized experimentally in a Rydberg-atom quantum simulator. In the experiment, long-lived coherent many-body oscillations were observed only when the system was initialized in a particular product state. This pronounced coherence has been attributed to the presence of special "scarred" eigenstates with nearly equally-spaced energies and putative nonergodic properties despite their finite energy density. In this paper we uncover a surprising connection between these scarred eigenstates and low-lying quasiparticle excitations of the spin chain. In particular, we show that these eigenstates can be accurately captured by a set of variational states containing a macroscopic number of magnons with momentum π. This leads to an interpretation of the scarred eigenstates as finite-energy-density condensates of weakly interacting π-magnons. One natural consequence of this interpretation is that the scarred eigenstates possess long-range order in both space and time, providing a rare example of the spontaneous breaking of continuous time-translation symmetry. We verify numerically the presence of this space-time crystalline order and explain how it is consistent with established no-go theorems precluding its existence in ground states and at thermal equilibrium.
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Phase transition of fractional Chern insulators: QED3 and beyond
Yin-Chen He Perimeter Institute for Theoretical Physics
Recent experiments in graphene heterostructures have observed Chern insulators - integer and fractional Quantum Hall states made possible by a periodic substrate potential. Here we study theoretically that the competition between different Chern insulators, which can be tuned by the amplitude of the periodic potential, leads to a new family of quantum critical points described by QED3-Chern-Simons theory. At these critical points, Nf flavors of Dirac fermions interact through an emergent U(1) gauge theory at Chern-Simons level K, and remarkably, the entire family (with any Nf or K) can be realized at special values of the external magnetic field. I will talk about the physical properties and microscopic realization of those critical points. We propose experiments on Chern insulators that could resolve open questions in the study of 2+1 dimensional conformal field theories and test recent duality inspired conjectures. -
Application of Tensor Network States to Lattice Field Theories
Stefan Kuhn Deutsches Elektronen-Synchrotron DESY
The conventional Euclidean time Monte Carlo approach to Lattice Field Theories faces a major obstacle in the sign problem in certain parameter regimes, such as the presence of a nonzero chemical potential or a topological theta-term. Tensor Network States, a family of ansatzes for the efficient description of quantum many-body states, offer a promising alternative for addressing Lattice Field Theories in the Hamiltonian formulation. In particular, numerical methods based on Tensor Network states do not suffer from the sign problem which makes it possible to study scenarios which are not accessible with standard Monte Carlo methods. In this talk I will present some recent work demonstrating this capability using two (1+1)-dimensional models as a test bed. Studying the O(3) nonlinear sigma model at nonzero chemical potential and the Schwinger model with topological theta-term, I will show how Tensor Networks States accurately describe the low-energy spectrum and that numerical errors can be controlled well enough to make contact with continuum predictions. -
Dynamics of two-point correlation functions in quantum systems
Alvaro Alhambra Universidad Autonoma de Madrid
We give rigorous analytical results on the temporal behavior of two-point correlation functions (also known as dynamical response functions or Green’s functions) in quantum many body systems undergoing unitary dynamics. Using recent results from large deviation theory, we show that in a large class of models the correlation functions factorize at late times -> , thus proving that dissipation emerges out of the unitary dynamics of the system. We also show that the fluctuations around this late-time value are bounded by the purity of the thermal ensemble, which generally decays exponentially with system size. This conclusion connects the behavior of correlation functions to that of the late-time fluctuations of quenched systems out of equilibrium. For auto-correlation functions such as (as well as the symmetrized and anti-symmetrized versions) we provide an upper bound on the timescale at which they reach that factorized late time value. Remarkably, this bound is a function of local expectation values only, and does not increase with system size. As such it constraints, for instance, the behavior of current auto-correlation functions that appear in quantum transport. We give numerical examples that show that this bound is a good estimate in chaotic models, and argue that the timescale that appears can be understood in terms of an emergent fluctuation-dissipation theorem. Our study extends to further classes of two point functions such as the Kubo function of linear response theory, for which we give an analogous result. Joint work with Luis Pedro Garcia-Pintos and Jonathon Riddell -
Extracting conformal and superconformal data from critical quantum spin chains
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Ashley Milsted California Institute of Technology
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Yijian Zou Perimeter Institute for Theoretical Physics
Key to characterizing universality in critical systems is the identification of the RG fixed point, which is very often a conformal field theory (CFT). We show how to use lattice operators that mimic the Virasoro generators of conformal symmetry to systematically extract, from a generic critical quantum spin chain, a complete set of the conformal data (central charge, scaling dimensions of primary fields, OPE coefficients) specifying a 2D CFT. We further show that, in the case of an extended superconformal symmetry, one can construct lattice operators that mimic the generators of the superconformal algebra, which allows us to identify superconformal primary states. -
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Topological phases in Kitaev Materials
Yong-Baek Kim University of Toronto
We discuss recent progress in theory and experiment on emergent topological phases in Kitaev materials. Here the competition between different anisotropic spin-exchange interactions may lead to a number of exotic phases of matter. We investigate possible emergence of quantum spin liquid, topological magnons, and topological superconductivity in two and three dimensional systems. We make connections to existing and future experiments. -
Finite Correlation Length Scaling in Lorentz-Invariant Gapless iPEPS Wave Functions
Andreas Lauchli Paul Scherrer Institute
It is an open question how well tensor network states in the form of an infinite projected entangled-pair states (iPEPS) tensor network can approximate gapless quantum states of matter. In this talk we address this issue for two different physical scenarios: (i) a conformally invariant (2+1)d quantum critical point in the incarnation of the transverse-field Ising model on the square lattice and (ii) spontaneously broken continuous symmetries with gapless Goldstone modes exemplified by the S=1/2 antiferromagnetic Heisenberg and XY models on the square lattice. We find that the energetically best wave functions display finite correlation lengths and we introduce a powerful finite correlation length scaling framework for the analysis of such finite bond dimension (finite-D) iPEPS states. The framework is important (i) to understand the mild limitations of the finite-D iPEPS manifold in representing Lorentz-invariant, gapless many-body quantum states and (ii) to put forward a practical scheme in which the finite correlation length ξ(D) combined with field theory inspired formulas can be used to extrapolate the data to infinite correlation length, i.e., to the thermodynamic limit. The finite correlation length scaling framework opens the way for further exploration of quantum matter with an (expected) Lorentz-invariant, massless low-energy description, with many applications ranging from condensed matter to high-energy physics. -
Shortcuts in Real and Imaginary Time
Timothy Hsieh Perimeter Institute for Theoretical Physics
In the first half, I will demonstrate an efficient and general approach for realizing non-trivial quantum states, such as quantum critical and topologically ordered states, in quantum simulators. In the second half, I will present a related variational ansatz for many-body quantum systems that is remarkably efficient. In particular, representing the critical point of the one-dimensional transverse field Ising model only requires a number of variational parameters scaling logarithmically with system size. Though optimizing the ansatz generally requires Monte Carlo sampling, our ansatz potentially enables a partial mitigation of the sign problem at the expense of having to optimize a few parameters. -
Isometric Tensor Network States in Two Dimensions
Michael Zaletel University of California, Berkeley
We introduce an isometric restriction of the tensor-network ansatz that allows for highly efficient contraction of the network. We consider two concrete applications using this ansatz. First, we show that a matrix-product state representation of a 2D quantum state can be iteratively transformed into an isometric 2D tensor network. Second, we introduce a 2D version of the time-evolving block decimation algorithm (TEBD2) for approximating the ground state of a Hamiltonian as an isometric tensor network, which we demonstrate for the 2D transverse field Ising model.