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Gopakumar R.,International Center for Theoretical science | Kaviraj A.,Indian Institute of Science | Sen K.,Indian Institute of Science | Sen K.,University of Tokyo | Sinha A.,Indian Institute of Science
Physical Review Letters | Year: 2017

We propose a new approach towards analytically solving for the dynamical content of conformal field theories (CFTs) using the bootstrap philosophy. This combines the original bootstrap idea of Polyakov with the modern technology of the Mellin representation of CFT amplitudes. We employ exchange Witten diagrams with built-in crossing symmetry as our basic building blocks rather than the conventional conformal blocks in a particular channel. Demanding consistency with the operator product expansion (OPE) implies an infinite set of constraints on operator dimensions and OPE coefficients. We illustrate the power of this method in the ϵ expansion of the Wilson-Fisher fixed point by reproducing anomalous dimensions and, strikingly, obtaining OPE coefficients to higher orders in ϵ than currently available using other analytic techniques (including Feynman diagram calculations). Our results enable us to get a somewhat better agreement between certain observables in the 3D Ising model and the precise numerical values that have been recently obtained. © 2017 American Physical Society.

Kawai H.,Kyoto University | Yokokura Y.,International Center for Theoretical science
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2016

We analyze time evolution of a spherically symmetric collapsing matter from a point of view that black holes evaporate by nature. We first consider a spherical thin shell that falls in the metric of an evaporating Schwarzschild black hole of which the radius a(t) decreases in time. The important point is that the shell can never reach a(t) but it approaches a(t)-a(t)da(t)dt. This situation holds at any radius because the motion of a shell in a spherically symmetric system is not affected by the outside. In this way, we find that the collapsing matter evaporates without forming a horizon. Nevertheless, a Hawking-like radiation is created in the metric, and the object looks the same as a conventional black hole from the outside. We then discuss how the information of the matter is recovered. We also consider a black hole that is adiabatically grown in the heat bath and obtain the interior metric. We show that it is the self-consistent solution of Gμν=8πG〈Tμν〉 and that the four-dimensional Weyl anomaly induces the radiation and a strong angular pressure. Finally, we analyze the internal structures of the charged and the slowly rotating black holes. © 2016 American Physical Society.

Das S.G.,Raman Research Institute | Dhar A.,International Center for theoretical science | Narayan O.,University of California at Santa Cruz
Journal of Statistical Physics | Year: 2014

Recent simulation results on heat conduction in a one-dimensional chain with an asymmetric inter-particle interaction potential and no onsite potential found non-anomalous heat transport in accordance to Fourier's law. This is a surprising result since it was long believed that heat conduction in one-dimensional systems is in general anomalous in the sense that the thermal conductivity diverges as the system size goes to infinity. In this paper we report on detailed numerical simulations of this problem to investigate the possibility of a finite temperature phase transition in this system. Our results indicate that the unexpected results for asymmetric potentials is a result of insufficient chain length, and does not represent the asymptotic behavior. © 2013 Springer Science+Business Media New York.

Mishra T.,International Center for Theoretical science | Pai R.V.,Goa University | Mukerjee S.,Indian Institute of Science
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2014

We study a system of hard-core boson on a one-dimensional lattice with frustrated next-nearest-neighbor hopping and nearest-neighbor interaction. At half filling, for equal magnitude of nearest- and next-nearest-neighbor hopping, the ground state of this system exhibits a first-order phase transition from a bond-ordered solid to a charge-density-wave solid as a function of the nearest-neighbor interaction. Moving away from half filling we investigate the system at incommensurate densities, where we find a supersolid phase which has concurrent off-diagonal long-range order and density-wave order which is unusual in a system of hard-core bosons in one dimension. Using the finite-size density-matrix renormalization group method, we obtain the complete phase diagram for this model. © 2014 American Physical Society.

Wu S.,University of Toronto | Wu S.,University of Waterloo | Killi M.,University of Toronto | Paramekanti A.,University of Toronto | And 2 more authors.
Physical Review B - Condensed Matter and Materials Physics | Year: 2012

Superlattices (SLs) in monolayer and bilayer graphene, formed by spatially periodic potential variations, lead to a modified bandstructure with extra finite-energy and zero-energy Dirac fermions with tunable anisotropic velocities. We theoretically show that transport in a weak perpendicular (orbital) magnetic field allows one to not only probe the number of emergent Dirac points but also yields further information about their dispersion. For monolayer graphene, we find that a moderate magnetic field can lead to a strong reversal of the transport anisotropy imposed by the SL potential, an effect that arises due to the SL-induced dispersion of the zero-energy Landau levels. This effect may find useful applications in switching or other devices. For bilayer graphene, we discuss the structure of Landau level wave functions and local density of states in the presence of a uniform bias, as well as in the presence of a kink in the bias that leads to topologically bound "edge states." We consider implications of these results for scanning tunneling spectroscopy measurements, valley filtering, and impurity-induced breakdown of the quantum Hall effect in bilayer graphene. © 2012 American Physical Society.

Singh M.,Indian Institute of Astrophysics | Dhar A.,Indian Institute of Astrophysics | Mishra T.,International Center for Theoretical science | Pai R.V.,Goa University | Das B.P.,Indian Institute of Astrophysics
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2012

The Mott-insulator-superfluid transition for ultracold bosonic atoms in an optical lattice has been extensively studied in the framework of the Bose-Hubbard model with two-body on-site interactions. In this paper, we analyze the additional effect of the three-body on-site interactions on this phase transition in an optical lattice and the transitions between the various phases that arise in an optical superlattice. Using the mean-field theory and the density matrix renormalization group method, we find the phase diagrams depicting the relationships between various physical quantities in an optical lattice and superlattice. We also propose a possible experimental signature to observe the on-site three-body interactions. © 2012 American Physical Society.

Mishra T.,International Center for Theoretical science | Pai R.V.,Goa University | Mukerjee S.,Indian Institute of Science | Paramekanti A.,University of Toronto | Paramekanti A.,Canadian Institute for Advanced Research
Physical Review B - Condensed Matter and Materials Physics | Year: 2013

Kinetically frustrated bosons at half filling in the presence of a competing nearest-neighbor repulsion support a wide supersolid regime on the two-dimensional triangular lattice. We study this model on a two-leg ladder using the finite-size density-matrix renormalization-group method, obtaining a phase diagram which contains three phases: a uniform superfluid (SF), an insulating charge density wave (CDW) crystal, and a bond ordered insulator (BO). We show that the transitions from SF to CDW and SF to BO are continuous in nature, with critical exponents varying continuously along the phase boundaries, while the transition from CDW to BO is found to be first order. The phase diagram is also found to contain an exactly solvable Majumdar Ghosh point, and reentrant SF to CDW phase transitions. © 2013 American Physical Society.

Dhar A.,International Center for Theoretical science | Saito K.,Keio University | Derrida B.,University Paris Diderot
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2013

The Lévy walk model is studied in the context of the anomalous heat conduction of one-dimensional systems. In this model, the heat carriers execute Lévy walks instead of normal diffusion as expected in systems where Fourier's law holds. Here we calculate exactly the average heat current, the large deviation function of its fluctuations, and the temperature profile of the Lévy walk model maintained in a steady state by contact with two heat baths (the open geometry). We find that the current is nonlocally connected to the temperature gradient. As observed in recent simulations of mechanical models, all the cumulants of the current fluctuations have the same system-size dependence in the open geometry. For the ring geometry, we argue that a size-dependent cutoff time is necessary for the Lévy walk model to behave like mechanical models. This modification does not affect the results on transport in the open geometry for large enough system sizes. © 2013 American Physical Society.

Hegde C.,Raman Research Institute | Sabhapandit S.,Raman Research Institute | Dhar A.,International Center for Theoretical science
Physical Review Letters | Year: 2014

We consider a gas of point particles moving in a one-dimensional channel with a hard-core interparticle interaction that prevents particle crossings - this is called single-file motion. Starting from equilibrium initial conditions we observe the motion of a tagged particle. It is well known that if the individual particle dynamics is diffusive, then the tagged particle motion is subdiffusive, while for ballistic particle dynamics, the tagged particle motion is diffusive. Here we compute the exact large deviation function for the tagged particle displacement and show that this is universal, independent of the individual dynamics. © 2014 American Physical Society.

Sabhapandit S.,Raman Research Institute | Dhar A.,International Center for Theoretical science
Journal of Statistical Mechanics: Theory and Experiment | Year: 2015

We consider a gas of point particles moving on the one-dimensional line with a hard-core inter-particle interaction that prevents particle crossings - this is usually referred to as single-file motion. The individual particle dynamics can be arbitrary and they only interact when they meet. Starting from initial conditions such that particles are uniformly distributed, we observe the displacement of a tagged particle at time t, with respect to the initial position of another tagged particle, such that their tags differ by r. For r = 0, this is the usual well studied problem of the tagged particle motion. Using a mapping to a non-interacting particle system we compute the exact probability distribution function for the two-tagged particle displacement, for general single particle dynamics. As by-products, we compute the large deviation function, various cumulants and, for the case of Hamiltonian dynamics, the two-particle velocity auto-correlation function. © 2015 IOP Publishing Ltd and SISSA Medialab srl.

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