From locally covariant QFT to quantum gravity
Katarzyna Rejzner University of York
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TBA
Antonello Scardicchio The Abdus Salam International Centre for Theoretical Physics (ICTP)
PIRSA:14050084 -
Gravity waves from Kerr/CFT
Achilleas Porfyriadis Harvard University
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Can Eigenstate Thermalization Breakdown without Disorder?
Matthew Fisher University of California, Santa Barbara
PIRSA:14050083 -
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:14050039 -
What can we learn from modifing gravity ?
Claudia de Rham Imperial College London
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Many-body mobility edge in a mean-field quantum spin-glass
Arijeet Pal Harvard University
PIRSA:14050078 -
Localization and topology protected quantum coherence at the edge of 'hot' matter
Ehud Altman University of California, Berkeley
PIRSA:14050077 -
Gapless spin liquids in frustrated Heisenberg models
Federico Becca SISSA International School for Advanced Studies
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From locally covariant QFT to quantum gravity
Katarzyna Rejzner University of York
Locally covariant quantum field theory (LCQFT) has proven to be a very successful framework for QFT on curved spacetimes. It is natural to ask, how far these ideas can be generalized and if one can learn something about quantum gravity, using LCQFT methods. In particular, one can use the relative Cauchy evolution to formulate the notion of background independence. Recently we have proven that background independence in this sense holds for effective quantum gravity, formulated as a perturbative QFT. Remarkably, the formalism of LCQFT can be extended to structures more general than spacetimes. The essential feature is the presence of the causal structure. An example application would be QFT on causal sets (work in progress). -
TBA
Antonello Scardicchio The Abdus Salam International Centre for Theoretical Physics (ICTP)
PIRSA:14050084 -
Gravity waves from Kerr/CFT
Achilleas Porfyriadis Harvard University
Astronomical observation suggests the existence of near-extreme Kerr black holes whose horizons spin at nearly the speed of light. Properties of diffeomorphisms imply that the dynamics of the high-redshift near-horizon region of near-extreme Kerr, which includes the innermost-stable-circular-orbit (ISCO), is governed by an infinite-dimensional emergent conformal symmetry. This symmetry may be exploited to analytically, rather than numerically, compute a variety of potentially observable processes. In this talk I will show how we compute and study the conformal transformation properties of the gravitational radiation emitted by an orbiting massive object in the large-redshift near-horizon region. I will also use conformal symmetry of the near-horizon region to compute the gravitational radiation produced during the plunge phase following the object's crossing of the ISCO. -
Can Eigenstate Thermalization Breakdown without Disorder?
Matthew Fisher University of California, Santa Barbara
PIRSA:14050083We describe a new diagnostic for many-body wavefunctions which generalizes the spatial bipartite entanglement entropy. By was of illustration, for a two-component wavefunction of heavy and light particles, a partial (projective) measurement of the coordinates of the heavy (but not light) particles is first performed, and then the entanglement entropy of the projected wavefunction for the light particles is computed. If the two-component wavefunction has a volume law entanglement entropy, yet the post measurement wavefunction of the light particles is disentangled with an area law entanglement, we refer to the original wavefunction as a “Quantum Disentangled State”. This diagnostic can be generalized to include other partial measurements, such as measuring the charge, but not spin, for finite-energy density eigenstates of Fermion Hubbard-type model. Quantum disentanglement results if the post measurement spin-wavefunction has an area law entanglement entropy. Recent numerics searching for such Quantum Disentangled States in 1d Hubbard-type models will be discussed in detail. -
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. -
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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).