On Mutual Information in Multipartite Quantum States and Equality in Strong Subadditivity of Entropy

The challenge of equality in the strong subadditivity inequality of entropy is approached via a general additivity of correlation information in terms of nonoverlapping clusters of subsystems in multipartite states (density operators). A family of tripartite states satisfying equality is derived.Comment: 8 pages; Latex2e and Revtex

Quantum critical points with the Coulomb interaction and the dynamical exponent: when and why z=1

A general scenario that leads to Coulomb quantum criticality with the dynamical critical exponent z=1 is proposed. I point out that the long-range Coulomb interaction and quenched disorder have competing effects on z, and that the balance between the two may lead to charged quantum critical points at which z=1 exactly. This is illustrated with the calculation for the Josephson junction array Hamiltonian in dimensions D=3-\epsilon. Precisely in D=3, however, the above simple result breaks down, and z>1. Relation to other theoretical studies is discussed.Comment: RevTex, 4 pages, 1 ps figur

Pseudo-magnetic catalysis of the time-reversal symmetry breaking in graphene

Finite flux of the (time-reversal-symmetric) pseudo-magnetic field, which represents the effect of wrinkling of the graphene sheet for example, is shown to be a catalyst for spontaneous breaking of the time-reversal symmetry of Dirac fermions in two dimensions. Possible experimental consequences of this effect for graphene are discussed.Comment: 4 revtex pages; improved presentation, updated reference

Conductivity of interacting massless Dirac particles in graphene: Collisionless regime

We provide detailed calculation of the a.c. conductivity in the case of 1/r-Coulomb interacting massless Dirac particles in graphene in the collisionless limit when \omega >> T. The analysis of the electron self-energy, current vertex function and polarization function, which enter into the calculation of physical quantities including the a.c. conductivity, is carried out by checking the Ward-Takahashi identities associated with the electrical charge conservation and making sure that they are satisfied at each step. We adopt a variant of the dimensional regularization of Veltman and t'Hooft by taking the spatial dimension D=2-\epsilon, for \epsilon > 0. The procedure adopted here yields a result for the conductivity correction which, while explicitly preserving charge conservation laws, is nevertheless different from the results reported previously in literature.Comment: 32 pages, no figures, published versio

Chiral symmetry breaking in QED3{\rm QED}_{3} in presence of irrelevant interactions: a renormalization group study

Motivated by recent theoretical approaches to high temperature superconductivity, we study dynamical mass generation in three dimensional quantum electrodynamics ${\rm QED}_{3}$) in presence of irrelevant four-fermion quartic terms. The problem is reformulated in terms of the renormalization group flows of certain four-fermion couplings and charge, and then studied in the limit of large number of fermion flavors $N$. We find that the critical number of fermions $N_c$ below which the mass becomes dynamically generated depends continuously on a weak chiral-symmetry-breaking interaction. One-loop calculation in our gauge-invariant approach yields $N_{c0} = 6$ in pure ${\rm QED}_3$. We also find that chiral-symmetry-preserving mass cannot become dynamically generated in pure ${\rm QED}_{3}$.Comment: 7 pages, 7 figure

Finite temperature transport at the superconductor-insulator transition in disordered systems

I argue that the incoherent, zero-frequency limit of the universal crossover function in the temperature-dependent conductivity at the superconductor-insulator transition in disordered systems may be understood as an analytic function of dimensionality of system d, with a simple pole at d=1. Combining the exact result for the crossover function in d=1 with the recursion relations in d=1+\epsilon, the leading term in the Laurent series in the small parameter \epsilon for this quantity is computed for the systems of disordered bosons with short-range and Coulomb interactions. The universal, low-temperature, dc critical conductivity for the dirty boson system with Coulomb interaction in d=2 is estimated to be 0.69 (2e)^2 /h, in relatively good agreement with many experiments on thin films. The next order correction is likely to somewhat increase the result, possibly bringing it closer to the self-dual value.Comment: 9 pages, LaTex, no figure

QED_3 theory of underdoped high temperature superconductors II: the quantum critical point

We study the effect of gapless quasiparticles in a d-wave superconductor on the T=0 end point of the Kosterlitz-Thouless transition line in underdoped high-temperature superconductors. Starting from a lattice model that has gapless fermions coupled to 3D XY phase fluctuations of the superconducting order parameter, we propose a continuum field theory to describe the quantum phase transition between the d-wave superconductor and the spin-density-wave insulator. Without fermions the theory reduces to the standard Higgs scalar electrodynamics (HSE), which is known to have the critical point in the inverted XY universality class. Extending the renormalization group calculation for the HSE to include the coupling to fermions, we find that the qualitative effect of fermions is to increase the portion of the space of coupling constants where the transition is discontinuous. The critical exponents at the stable fixed point vary continuously with the number of fermion fields $N$, and we estimate the correlation length exponent (nu = 0.65) and the vortex field anomalous dimension(eta_Phi=-0.48) at the quantum critical point for the physical case N=2. The stable critical point in the theory disappears for the number of Dirac fermions N > N_c, with N_c ~ 3.4 in our approximation. We discuss the relationship between the superconducting and the chiral (SDW) transitions, and point to some interesting parallels between our theory and the Thirring model.Comment: 13 pages including figures in tex

Schwinger-Keldysh approach to out of equilibrium dynamics of the Bose Hubbard model with time varying hopping

We study the real time dynamics of the Bose Hubbard model in the presence of time-dependent hopping allowing for a finite temperature initial state. We use the Schwinger-Keldysh technique to find the real-time strong coupling action for the problem at both zero and finite temperature. This action allows for the description of both the superfluid and Mott insulating phases. We use this action to obtain dynamical equations for the superfluid order parameter as hopping is tuned in real time so that the system crosses the superfluid phase boundary. We find that under a quench in the hopping, the system generically enters a metastable state in which the superfluid order parameter has an oscillatory time dependence with a finite magnitude, but disappears when averaged over a period. We relate our results to recent cold atom experiments.Comment: 22 pages, 7 figure

Dirac Hamiltonians for bosonic spectra

Dirac materials are of great interest as condensed matter realizations of the Dirac and Weyl equations. In particular, they serve as a starting point for the study of topological phases. This physics has been extensively studied in electronic systems such as graphene, Weyl- and Dirac semi-metals. In contrast, recent studies have highlighted several examples of Dirac-like cones in collective excitation spectra, viz. in phonon, magnon and triplon bands. These cannot be directly related to the Dirac or Weyl equations as they are bosonic in nature with pseudo-unitary band bases. In this article, we show that any Dirac-like equation can be smoothly deformed into a form that is applicable to bosonic bands. The resulting bosonic spectra bear a two-to-one relation to that of the parent Dirac system. Their dispersions inherit several interesting properties including conical band touching points and a gap-opening-role for `mass' terms. The relationship also extends to the band eigenvectors with the bosonic states carrying the same Berry connections as the parent fermionic states. The bosonic bands thus inherit topological character as well. If the parent fermionic system has non-trivial topology that leads to mid-gap surface states, the bosonic analogue also hosts surface states that lie within the corresponding band gap. The proposed bosonic Dirac structure appears in several known models. In materials, it is realized in Ba$_2$CuSi$_2$O$_6$Cl$_2$ and possibly in CoTiO$_3$ as well as in paramagnetic honeycomb ruthenates. Our results allow for a rigorous understanding of Dirac phononic and magnonic systems and enable concrete predictions, e.g., of surface states in magnonic topological insulators and Weyl semi-metals.Comment: 10 pages, supersedes arXiv:1802.0826

Antiferromagnetism from phase disordering of a d-wave superconductor

The unbinding of vortex defects in the superconducting condensate with d-wave symmetry at T=0 is shown to lead to the insulator with incommensurate spin-density-wave order. The transition is similar to the spontaneous generation of the "chiral" mass in the three dimensional quantum electrodynamics, at which the global chiral symmetry one can define in the superconducting state is spontaneously broken. Other symmetry related states and possible relations to recent experiments on uderdoped cuprates are briefly discussed.Comment: RevTex, 4 pages, one ps figure; comments on confinement in the SDW added, references updated; final versio