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Molina-Vilaplanaa J.,Technical University of Cartagena | Sodanob P.,Perimeter Institute of Theoretical Physics | Sodanob P.,University of Perugia
Journal of High Energy Physics | Year: 2011

In (d + 1) dimensional Multiscale Entanglement Renormalization Ansatz (MERA) networks, tensors are connected so as to reproduce the discrete, (d + 2) holographic geometry of Anti de Sitter space (AdSd+2) with the original system lying at the boundary. We analyze the MERA renormalization flow that arises when computing the quantum correlations between two disjoint blocks of a quantum critical system, to show that the structure of the causal cones characteristic of MERA, requires a transition between two different regimes attainable by changing the ratio between the size and the separation of the two disjoint blocks. We argue that this transition in the MERA causal developments of the blocks may be easily accounted by an AdSd+2 black hole geometry when the mutual information is computed using the Ryu-Takayanagi formula. As an explicit example, we use a BTZ AdS3 black hole to compute the MI and the quantum correlations between two disjoint intervals of a one dimensional boundary critical system. Our results for this low dimensional system not only show the existence of a phase transition emerging when the conformal four point ratio reaches a critical value but also provide an intuitive entropic argument accounting for the source of this instability. We discuss the robustness of this transition when finite temperature and finite size effects are taken into account. © 2011 SISSA.

Chowdhury D.,Harvard University | Sachdev S.,Harvard University | Sachdev S.,Perimeter Institute of Theoretical Physics
Physical Review B - Condensed Matter and Materials Physics | Year: 2015

We analyze a candidate theory for the strange metal near optimal hole doping in the cuprate superconductors. The theory contains a quantum phase transition between metals with large and small Fermi surfaces of spinless fermions carrying the electromagnetic charge of the electron, but the transition does not directly involve any broken global symmetries. The two metals have emergent SU(2) and U(1) gauge fields respectively, and the transition is driven by the condensation of a real Higgs field, carrying a finite lattice momentum and an adjoint SU(2) gauge charge. This Higgs field measures the local antiferromagnetic correlations in a "rotating reference frame." We propose a global phase diagram around this Higgs transition, and describe its relationship to a variety of recent experiments on the cuprate superconductors. © 2015 American Physical Society.

Bose S.,University College London | Sodano P.,University of Perugia | Sodano P.,Perimeter Institute of Theoretical Physics
New Journal of Physics | Year: 2011

We show that a one-dimensional device supporting a pair of Majorana bound states (MBS) at its ends can produce remarkable Hanbury-Brown-Twiss-like interference effects between well-separated Dirac fermions of pertinent energies. We find that the simultaneous scattering of two incoming electrons or two incoming holes from the MBS leads exclusively to an electron-hole final state. This 'anti-bunching' in electron-hole internal pseudospin space can be detected through current-current correlations. Further, we show that, by scattering appropriate spin-polarized electrons from the MBS, one can engineer a non-local entangler of electronic spins for quantum information applications. Both the above phenomena should be observable in diverse physical systems enabling us to detect the presence of low-energy Majorana modes. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

Swingle B.,Harvard University | Kim I.H.,Perimeter Institute of Theoretical Physics | Kim I.H.,University of Waterloo
Physical Review Letters | Year: 2014

We consider the problem of reconstructing global quantum states from local data. Because the reconstruction problem has many solutions in general, we consider the reconstructed state of maximum global entropy consistent with the local data. We show that unique ground states of local Hamiltonians are exactly reconstructed as the maximal entropy state. More generally, we show that if the state in question is a ground state of a local Hamiltonian with a degenerate space of locally indistinguishable ground states, then the maximal entropy state is close to the ground state projector. We also show that local reconstruction is possible for thermal states of local Hamiltonians. Finally, we discuss a procedure to certify that the reconstructed state is close to the true global state. We call the entropy of our reconstructed maximum entropy state the "reconstruction entropy," and we discuss its relation to emergent geometry in the context of holographic duality. © 2014 American Physical Society.

Freivogel B.,University of Amsterdam | Yang I.-S.,Perimeter Institute of Theoretical Physics
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2016

We analyze the gravitational dynamics of a classical scalar field coupled to gravity in asymptotically AdS spacetime, which leads to black hole formation on the shortest nonlinear time scale for some initial conditions. We show that the observed collapse cannot be described by the well-known process of a random-phase cascade in the theory of weak turbulence. This implies that the dynamics on this time scale is highly sensitive to the phases of modes. We explore the alternative possibility of a coherent phase cascade and analytically find stationary solutions with completely coherent phases and power-law energy spectra. We show that these power-law spectra lead to diverging geometric backreaction, which is the likely precursor to black hole formation. In 4+1 dimensions, our stationary solution has the same power-law energy spectrum as the final state right before collapse observed in numerical simulations. We conjecture that our stationary solutions describe the system shortly before collapse in other dimensions, and predict the energy spectrum. © 2016 American Physical Society.

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