Universal dynamics and topological order in many-body localized states
Ronen Vosk Weizmann Institute of Science
PIRSA:14050082
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A polynomial-time algorithm for the ground state of 1D gapped local Hamiltonians
Thomas Vidick Weizmann Institute of Science
PIRSA:14050039What can we learn from modifing gravity ?
Claudia de Rham Imperial College London
Many-body mobility edge in a mean-field quantum spin-glass
Arijeet Pal Harvard University
PIRSA:14050078Localization and topology protected quantum coherence at the edge of 'hot' matter
Ehud Altman University of California, Berkeley
PIRSA:14050077Gapless spin liquids in frustrated Heisenberg models
Federico Becca SISSA International School for Advanced Studies
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)
New strong interactions and the t t-bar asymmetry
Joachim Brod University of Cincinnati
Long-time behavior of periodically driven isolated interacting quantum systems
Luca D'Alessio Boston University
PIRSA:14050073
Universal dynamics and topological order in many-body localized states
Ronen Vosk Weizmann Institute of Science
PIRSA:14050082It has been argued recently that, through a phenomenon of many-body localization, closed quantum systems subject to sufficiently strong disorder would fail to thermalize. In this talk I will describe a real time renormalization group approach, which offers a controlled description of universal dynamics in the localized phase. In particular it explains the ultra-slow entanglement propagation in this state and identifies the emergent conserved quantities which prevent thermalization. The RG analysis also shows, that far from being a trivial dead state, the MBL state admits phase transitions between distinct dynamical phases. For example, I will discuss the universal aspects of a transition between a paramagnetic localized state to one which exhibits spin-glass order. Finally, I will present a development of the RG scheme, defined on an effective coarse grained model, which allows to capture the transition from a many-body localized to a thermalizing state.A polynomial-time algorithm for the ground state of 1D gapped local Hamiltonians
Thomas Vidick Weizmann Institute of Science
PIRSA:14050039Computing ground states of local Hamiltonians is a fundamental problem in condensed matter physics. We give the first randomized polynomial-time algorithm for finding ground states of gapped one-dimensional Hamiltonians: it outputs an (inverse-polynomial) approximation, expressed as a matrix product state (MPS) of polynomial bond dimension. The algorithm combines many ingredients, including recently discovered structural features of gapped 1D systems, convex programming, insights from classical algorithms for 1D satisfiability, and new techniques for manipulating and bounding the complexity of MPS. Our result provides one of the first major classes of Hamiltonians for which computing ground states is provably tractable despite the exponential nature of the objects involved. /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-style-parent:""; font-size:11.0pt; font-family:"Calibri","sans-serif";}What can we learn from modifing gravity ?
Claudia de Rham Imperial College London
I will review models of modified gravity in the infrared and show how extra degrees of freedom present in these theories get screened via the Vainshtein mechanism. That mechanism comes hand in hand with its own share of peculiarities: classical superluminalities, strong coupling and perturbative non-analyticity of the S-matrix to name a few. From a traditional effective field viewpoint such effects are disastrous but I will present the first hints in understanding these theories beyond the traditional perspective and their implications not only for gravity but also for our understanding of a certain class of field theories.A Rigorous Result on Many-Body Localization
John Imbrie University of Virginia
PIRSA:14050079I will discuss a proof of many-body localization for a one-dimensional spin chain with random local interactions. The proof depends on a physically reasonable assumption that limits the amount of level attraction in the system. I construct a sequence of local rotations that completely diagonalizes the Hamiltonian and exhibits the local degrees of freedom.Many-body mobility edge in a mean-field quantum spin-glass
Arijeet Pal Harvard University
PIRSA:14050078Isolated, interacting quantum systems in the presence of strong disorder can exist in a many-body localized phase where the assumptions of equilibrium statistical physics are violated. On tuning either the parameters of the Hamiltonian or the energy density, the system is expected to transition into the ergodic phase. While the transition at "infinite temperature" as a function of system parameters has been found numerically but, the transition tuned by energy density has eluded such methods.
In my talk I will discuss the nature of the many-body localization-delocalization (MBLD) transition as a function of energy denisty in the quantum random energy model (QREM). QREM provides a mean-field description of the equilibrium spin glass transition. We show that it further exhibits a many-body mobility edge when viewed as a closed quantum system. The mean-field structure of the model allows an analytically tractable description of the MBLD transition. I will also comment on the nature of the critical states in this mean-field model.
This opens the possibility of developing a mean-field theory of this interesting dynamical phase transition.Localization and topology protected quantum coherence at the edge of 'hot' matter
Ehud Altman University of California, Berkeley
PIRSA:14050077Topological phases are often characterized by special edge states confined near the boundaries by an energy gap in the bulk. On raising temperature, these edge states are lost in a clean system due to mobile thermal excitations. Recently however, it has been established that disorder can localize an isolated many body system, potentially allowing for a sharply defined topological phase even in a highly excited state.I will show this to be the case for the topological phase of a one dimensional magnet with quenched disorder, which features spin one-half excitations at the edges. The time evolution of a simple, highly excited, initial state is used to reveal quantum coherent edge spins. In particular, I will demonstrate, using theoretical arguments and numerical simulation, the coherent revival of an edge spin over a time scale that grows exponentially bigger with system size. This is in sharp contrast to the general expectation that quantum bits strongly coupled to a 'hot' many body system will rapidly lose coherence.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.