Perimeter Institute of Theoretical Physics

Waterloo, Canada

Perimeter Institute of Theoretical Physics

Waterloo, Canada
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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.

News Article | February 5, 2016

New findings from an international collaboration led by Canadian scientists may eventually lead to a theory of how superconductivity initiates at the atomic level, a key step in understanding how to harness the potential of materials that could provide lossless energy storage, levitating trains and ultra-fast supercomputers. Professor David Hawthorn, Professor Michel Gingras, doctoral student Andrew Achkar, and post-doctoral fellow Dr. Zhihao Hao from University of Waterloo's Department of Physics and Astronomy have experimentally shown that electron clouds in superconducting materials can snap into an aligned and directional order called nematicity. "It has become apparent in the past few years that the electrons involved in superconductivity can form patterns, stripes or checkerboards, and exhibit different symmetries - aligning preferentially along one direction," said Professor Hawthorn. "These patterns and symmetries have important consequences for superconductivity - they can compete, coexist or possibly even enhance superconductivity. " Their results, published today in the prestigious journal Science, present the most direct experimental evidence to date of electronic nematicity as a universal feature in cuprate high-temperature superconductors. "In this study, we identify some unexpected alignment of the electrons - a finding that is likely generic to the high temperature superconductors and in time may turn out be a key ingredient of the problem," said Professor Hawthorn. Superconductivity, the ability of a material to conduct an electric current with zero resistance, is best described as an exotic state in high temperature superconductors - challenging to predict, let alone explain. The scientists used a novel technique called soft x-ray scattering at the Canadian Light Source synchrotron in Saskatoon to probe electron scattering in specific layers in the cuprate crystalline structure. Specifically, the individual cuprate (CuO2) planes, where electronic nematicity takes place, versus the crystalline distortions in between the CuO2 planes. Electronic nematicity happens when the electron orbitals align themselves like a series of rods - breaking their unidirectional symmetry apart from the symmetry of the crystalline structure. The term "nematicity" commonly refers to when liquid crystals spontaneously align under an electric field in liquid crystal displays. In this case, it is the electronic orbitals that enter the nematic state as the temperature drops below a critical point. Recent breakthroughs in high-temperature superconductivity have revealed a complex competition between the superconductive state and charge density wave order fluctuations. These periodic fluctuations in the distribution of the electrical charges create areas where electrons bunch up in high- versus low-density clouds, a phenomenon that is now recognized to be generic to the underdoped cuprates. Results from this study show electronic nematicity also likely occurs in underdoped cuprates. Understanding the relation of nematicity to charge density wave order, superconductivity and an individual material's crystalline structure could prove important to identifying the origins of the superconducting and so-called pseudogap phases. The authors also found the choice of doping material impacts the transition to the nematic state. Dopants, such as strontium, lanthanum, and even europium added to the cuprate lattice, create distortions in the lattice structure which can either strengthen or weaken nematicity and charge density wave order in the CuO2 layer. Although there is not yet an agreed upon explanation for why electronic nematicity occurs, it may ultimately present another knob to tune in the quest to achieve the ultimate goal of a room temperature superconductor. "Future work will tackle how electronic nematicity can be tuned, possibly to advantage, by modifying the crystalline structure," says Hawthorn. Hawthorn and Gingras are both Fellows of the Canadian Institute For Advanced Research. Gingras holds the Canada Research Chair in Condensed Matter Theory and Statistical Mechanics and spent time at the Perimeter Institute of Theoretical Physics as a visiting researcher while this work was being carried out.

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.

Kim I.H.,California Institute of Technology | Kim I.H.,Perimeter Institute of Theoretical Physics | Kim I.H.,University of Waterloo
Physical Review B - Condensed Matter and Materials Physics | Year: 2014

We propose an order parameter for a general one-dimensional gapped system with an open boundary condition. The order parameter can be computed from the ground state entanglement entropy of some regions near one of the boundaries. Hence, it is well defined even in the presence of arbitrary interaction and disorder. We also show that it is invariant under a finite-depth local quantum circuit, suggesting its stability against an arbitrary local perturbation that does not close the energy gap. Further, it can unambiguously distinguish a Majorana chain from a trivial chain under global fermion parity conservation. We argue that the order parameter can be, in principle, measured in an optical lattice system. © 2014 American Physical Society.

Metlitski M.A.,University of California at Santa Barbara | Mross D.F.,California Institute of Technology | Sachdev S.,Harvard University | Sachdev S.,Perimeter Institute of Theoretical Physics | Senthil T.,Massachusetts Institute of Technology
Physical Review B - Condensed Matter and Materials Physics | Year: 2015

States of matter with a sharp Fermi surface but no well-defined Landau quasiparticles arise in a number of physical systems. Examples include (i) quantum critical points associated with the onset of order in metals; (ii) spinon Fermi-surface [U(1) spin-liquid] state of a Mott insulator; (iii) Halperin-Lee-Read composite fermion charge liquid state of a half-filled Landau level. In this work, we use renormalization group techniques to investigate possible instabilities of such non-Fermi liquids in two spatial dimensions to Cooper pairing. We consider the Ising-nematic quantum critical point as an example of an ordering phase transition in a metal, and demonstrate that the attractive interaction mediated by the order-parameter fluctuations always leads to a superconducting instability. Moreover, in the regime where our calculation is controlled, superconductivity preempts the destruction of electronic quasiparticles. On the other hand, the spinon Fermi surface and the Halperin-Lee-Read states are stable against Cooper pairing for a sufficiently weak attractive short-range interaction; however, once the strength of attraction exceeds a critical value, pairing sets in. We describe the ensuing quantum phase transition between (i) U(1) and Z2 spin-liquid states; (ii) Halperin-Lee-Read and Moore-Read states. © 2015 American Physical Society.

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.

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.

Clifton T.,University of Oxford | Zlosnik T.G.,Perimeter Institute of Theoretical Physics
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2010

We consider spatially homogeneous and isotropic Friedmann-Robertson-Walker solutions of Milgrom's recently proposed class of bimetric theories of gravity. These theories have two different regimes, corresponding to high and low acceleration. We find simple power-law matter dominated solutions in both, as well as solutions with spatial curvature, and exponentially expanding solutions. In the high acceleration limit these solutions behave like the Friedmann-Robertson-Walker solutions of general relativity, with a cosmological constant term that is of the correct order of magnitude to explain the observed accelerating expansion of the Universe. We find that solutions that remain in the high acceleration regime for their entire history, however, require nonbaryonic dark matter fields, or extra interaction terms in their gravitational Lagrangian, in order to be observationally viable. The low acceleration regime also provides some scope to account for this deficit, with solutions that differ considerably from their general relativistic counterparts. © 2010 The American Physical Society.

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.

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

Recent experiments in the underdoped regime of the hole-doped cuprates have found evidence for an incommensurate charge density-wave state. We present an analysis of the charge ordering instabilities in a metal with antiferromagnetic correlations, where the electronic excitations are coupled to the fractionalized excitations of a quantum fluctuating antiferromagnet on the square lattice. The resulting charge density-wave state emerging out of such a fractionalized Fermi liquid (FL∗) has wave vectors of the form (±Q0,0),(0,±Q0), with a predominantly d-form factor, in agreement with experiments on a number of different families of the cuprates. In contrast, as previously shown, the charge density-wave instability of a nearly antiferromagnetic metal with a large Fermi surface, interacting via short-range interactions, has wave vectors of the type (±Q0,±Q0). Our results show that the observed charge density-wave appears as a low-energy instability of a fractionalized metallic state linked to the proximity to an antiferromagnetic insulator, and the pseudogap regime can be described by such a metal at least over intermediate length and energy scales. © 2014 American Physical Society.

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