Gapless spin liquids in frustrated Heisenberg models
Federico Becca SISSA International School for Advanced Studies
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Unitarity and crossing symmetry in the S-matirx of large N Chern-Simons theory with fundamental matter
Shiraz Minwalla Tata Institute of Fundamental Research (TIFR)
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New strong interactions and the t t-bar asymmetry
Joachim Brod University of Cincinnati
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Long-time behavior of periodically driven isolated interacting quantum systems
Luca D'Alessio Boston University
PIRSA:14050073 -
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Light-Cone Effects after Quantum Quenches and Excitations at Finite Entropy
Fabian Essler University of Oxford
PIRSA:14050072 -
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The quest for self-correcting quantum memory
Olivier Landon-Cardinal California Institute of Technology
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Curvature in Noncommutative Geometry
masoud khalkhali Western University
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Gapless spin liquids in frustrated Heisenberg models
Federico Becca SISSA International School for Advanced Studies
We present our recent numerical calculations for the Heisenberg model on the square and
Kagome lattices, showing that gapless spin liquids may be stabilized in highly-frustrated
regimes. In particular, we start from Gutzwiller-projected fermionic states that may
describe magnetically disordered phases,[1] and apply few Lanczos steps in order to improve
their accuracy. Thanks to the variance extrapolation technique,[2] accurate estimations of
the energies are possible, for both the ground state and few low-energy excitations.
Our approach suggests that magnetically disordered phases can be described by Abrikosov
fermions coupled to gauge fields.
For the Kagome lattice, we find that a gapless U(1) spin liquid with Dirac cones
is competitive with previously proposed gapped spin liquids when only the nearest-neighbor
antiferromagnetic interaction is present.[3,4] The inclusion of a next-nearest-neighbor term
lead to a Z_2 gapped spin liquid,[5] in agreement with density-matrix renormalization group
calculations.[6] In the Heisenberg model on the square lattice with both nearest- and
next-nearest-neighbor interactions, a Z_2 spin liquid with gapless spinon excitations is
stabilized in the frustrated regime.[7] This results are (partially) in agreement with recent
density-matrix renormalization group on large cylinders.[8]
[1] X.-G. Wen, Phys. Rev. B {\bf 44}, 2664 (1991); Phys. Rev. B {\bf 65}, 165113 (2002).
[2] S. Sorella, Phys. Rev. B {\bf 64}, 024512 (2001).
[3] Y. Iqbal, F. Becca, S. Sorella, and D. Poilblanc, Phys. Rev. B 87, 060405(R) (2013).
[4] Y. Iqbal, D. Poilblanc, and F. Becca, Phys. Rev. B 89, 020407(R) (2014).
[5] W.-J. Hu, Y. Iqbal, F. Becca, D. Poilblanc, and D. Sheng, unpublished.
[6] H.-C. Jiang, Z. Wang, and L. Balents, Nat. Phys. 8, 902 (2012);
S. Yan, D. Huse, and S. White, Science 332, 1173 (2011).
[7] W.-J. Hu, F. Becca, A. Parola, and S. Sorella, Phys. Rev. B 88, 060402(R) (2013).
[8] S.-S. Gong, W.Z., D.N. Sheng, O.I. Motrunich, and M.P.A. Fisher, arXiv:1311.5962 (2013). -
Unitarity and crossing symmetry in the S-matirx of large N Chern-Simons theory with fundamental matter
Shiraz Minwalla Tata Institute of Fundamental Research (TIFR)
We present explicit computations and conjectures for 2 → 2 scattering matrices in large N U(N) Chern-Simons theories coupled to fundamental bosonic or fermionic matter to all orders in the ’t Hooft coupling expansion. The bosonic and fermionic S-matrices map to each other under the recently conjectured Bose-Fermi duality after a level-rank transposition. The S-matrices presented in this paper may be regarded as relativistic generalization of Aharonov-Bohm scattering. They have unusual structural features: they include a non analytic piece localized on forward scattering, and obey modified crossing symmetry rules. We conjecture that these unusual features are properties of S-matrices in all Chern-Simons matter theories. The S-matrix in one of the exchange channels in our paper has an anyonic character; the parameter map of the conjectured Bose-Fermi duality may be derived by equating the anyonic phase in the bosonic and fermionic theories. -
New strong interactions and the t t-bar asymmetry
Joachim Brod University of Cincinnati
The CDF and D0 experiments at Tevatron measure a top-quark forward-backward
asymmetry significantly larger than the standard-model prediction.
We construct a model that involves new strong interactions at the electroweak scale
and can explain the measured asymmetry. Our model possesses a flavor symmetry
which allows to evade flavor and collider constraints, while it still permits flavor-violating
couplings of order 1 which are needed to generate the asymmetry via light t-channel vectors. -
Long-time behavior of periodically driven isolated interacting quantum systems
Luca D'Alessio Boston University
PIRSA:14050073We show that generic interacting quantum systems, which are isolated and finite, periodically driven by sudden quenches exhibit three physical regimes. For short driving periods the Floquet Hamiltonian is well approximated by the time-averaged Hamiltonian, while for long periods the evolution operator exhibits properties of random matrices of a Circular Ensemble (CE). In-between, there is a crossover
regime. We argue that, in the thermodynamic limit and for nonvanishing driving periods, the evolution operator always exhibits properties of CE random matrices. Consequently, driving leads to infinite temperature at infinite time and to an unphysical Floquet Hamiltonian. -
Random models of inflation
Andrew Liddle University of Lisbon
Rather than writing down specific functional forms, one can generate inflation models via stochastic processes in order to explore generic properties of inflation models. I describe our explorations of the phenomenology of randomly-generated multi-field inflation models, both for canonical fields and for a braneworld-motivated scenario. Implications of some recent observational results, including BICEP2, will be discussed. -
Light-Cone Effects after Quantum Quenches and Excitations at Finite Entropy
Fabian Essler University of Oxford
PIRSA:14050072 -
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The quest for self-correcting quantum memory
Olivier Landon-Cardinal California Institute of Technology
A self-correcting quantum memory is a physical system whose quantum state can be preserved over a long period of time without the need for any external intervention. The most promising candidates are topological quantum systems which would protect information encoded in their degenerate groundspace while interacting with a thermal environment. Many models have been suggested but several approaches have been shown to fail due to no-go results of increasingly general scope. In a nutshell, 2D topological models and many 3D topological models have point-like excitations which propagate freely and change the groundstate at any non-zero temperature. A recent suggestion is to introduce effective long-range interactions between those point-like excitations. In this presentation, I will first explain the desiderata for self-correction, review the recent advances and no-go results, and describe the current endeavours to define a self-correcting system in 2D and 3D. Time permitting, I will briefly present our recent work on the thermal instability of models which aim to introduce effective long-range interactions between point-like excitations (joint work with Beni Yoshida, John Preskill and David Poulin). -
Dynamical analogue quantum simulators
Jens Eisert Freie Universität Berlin
PIRSA:14050068Complex quantum systems out of equilibrium are at the basis of a number of long-standing questions in physics. This talk will be concerned on the one hand with recent progress on understanding how quantum many-body systems out of equilibrium eventually come to rest, thermalise and cross phase transitions, on the other hand with dynamical analogue quantum simulations using cold atoms [1-4]. In an outlook, we will discuss the question of certification of quantum simulators, and will how this problem also arises in other related settings, such as in Boson samplers [5,6]. [1] S. Braun, M. Friesdorf, S. S. Hodgman, M. Schreiber, J. P. Ronzheimer, A. Riera, M. del Rey, I. Bloch, J. Eisert, U. Schneider, arXiv:1403.7199.
[2] M. Kliesch, M. Kastoryano, C. Gogolin, A. Riera, J. Eisert, arXiv:1309:0816.
[3] S. Trotzky, Y.-A. Chen, A. Flesch, I. P. McCulloch, U. Schollwoeck, J. Eisert, I. Bloch, Nature Physics 8, 325 (2012).
[4] A. Riera, C. Gogolin, M. Kliesch, J. Eisert, in preparation (2014).
[5] C. Gogolin, M. Kliesch, L. Aolita, J. Eisert, in preparation (2014) and arXiv:1306.3995.
[6] S. Aaronson, A. Arkhipov, arXiv:1309.7460. -
Quantum Quenches in Thermodynamic Limit
Marcos Rigol Pennsylvania State University
PIRSA:14050067Studies of the quantum dynamics of isolated systems are currently providing fundamental insights into how statistical mechanics emerges under unitary time evolution. Thermalization seems ubiquitous, but experiments with ultracold gases have shown that it need not always occur, particularly near an integrable point. Unfortunately, computational studies of generic (nonintegrable) models are limited to small systems, for which arbitrarily long times can be calculated, or short times, for which large or infinite system sizes can be solved. Consequently, what happens in the thermodynamic limit after long times has been inaccessible to theoretical studies. In this talk, we introduce a linked-cluster based computational approach that allows one to address the latter question in lattice systems. We provide numerical evidence that, in the thermodynamic limit, thermalization occurs in the nonintegrable regime but fails at integrability. A phase transition-like behavior separates the two regimes. -
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Curvature in Noncommutative Geometry
masoud khalkhali Western University
After the seminal work of Connes and Tretkoff on the Gauss-Bonnet theorem for the noncommutative 2-torus and its extension by Fathizadeh and myself, there have been significant developments in understanding the local differential geometry of these noncommutative spaces equipped with curved metrics. In this talk, I will review a series of joint works with Farzad Fathizadeh in which we compute the scalar curvature for curved noncommutative tori and prove the analogue of Weyl's law and Connes' trace theorem. Our final formula for the curvature matches precisely with the one computed independently by A. Connes and H. Moscovici. I will then report on our recent work on the computation of scalar curvature for noncommutative 4-tori (which involves intricacies due to violation of the Kähler condition). We show that metrics with constant curvature are extrema of the analogue of the Einstein–Hilbert action. A purely noncommutative feature in these works is the appearance of the modular automorphism from Tomita–Takesaki theory of KMS states in the final formulas for the curvature.