Zaira Nazario

Quantum states of matter of simple bosonic systems: BECs, superfluids and quantum solids

The phase diagram of a single component Bose system in a lattice at zero temperature is obtained. We calculate the variational energies for the Mott insulating and superfluid phases. Below a certain critical density the Mott insulating phase is stable over the superfluid phase for low enough tunneling amplitude regardless of whether the number of bosons is or is not incommensurate with the lattice. The transition is discontinuous as the superfluid order parameter jumps from a finite value to zero at the Mott transition.

On vortices and phase coherence in high-T c superconductors

An array of Cooper paired planes will not have long-range phase coherence at any finite temperature owing to an infrared divergence of phase fluctuations when the coherence length perpendicular to the plane is small enough to prevent leakage of the superconducting order parameter within the planes. The phase correlations decay in a sufficiently slow manner to provide enough local phase coherence to make possible the nucleation of vortices. The planes then acquire Kosterlitz–Thouless topological order with its intrinsic rigidity and concomitant superfluidity. We conclude that the high-temperature superconducting cuprates are topologically ordered superconductors rather than phase-ordered superconductors since the large insulating layer between the copper–oxygen planes prevents effective leakage of the superfluid order parameter. For low enough superfluid densities, as in the underdoped cuprates studied by Uemura, the transition temperature T c will be proportional to the superfluid density corresponding to vortex–antivortex unbinding, and not to the disappearance of the Cooper pairing amplitude. Above T c, but below the Bardeen–Cooper–Schrieffer pairing temperature T p, we shall have a dephased Cooper pair fluid that is a vortex–antivortex liquid. Since the superconductivity is effectively two dimensional, there can be a large difference between T p and T c, as observed in the underdoped cuprates. The ac and dc conductivities measured by Corson et al. in this region are those corresponding to flux flow. Furthermore there will be vortices over a large temperature region above T c which will lead to a Nernst vortex-like response and there will be a measurable depairing field above T c as evidenced by recent experiments by Wang et al.

Elementary Excitations of Quantum Critical (2 + 1)-Dimensional Antiferromagnets

It has been proposed that there are degrees of freedom intrinsic to quantum critical points that can contribute to quantum critical physics. We point out that this conclusion is quite general below the upper critical dimension. We show that in (2+1)D antiferromagnets Skyrmion excitations are stable at criticality and identify them as the critical excitations. We find exact solutions composed of Skyrmion and anti-Skyrmion superpositions, which we call topolons. We include the topolons in the partition function and renormalize by integrating out small size topolons and short wavelength spin waves. We obtain a correlation length exponent nu=0.690 666 and anomalous dimension eta=0.0166.

On Gossamer metals and insulating behaviour

We extend the Gossamer technique recently proposed to describe superconducting ground states to metallic ground states. The Gossamer metal in a single band model will describe a metallic phase that becomes arbitrarily hard to differentiate from an insulator as one turns the Coulomb correlations up. We were motivated by the phase diagram of V2O3 and f-electron systems which have phase diagrams in which a line of first-order metal–insulator transition ends at a critical point above which the two phases are indistinguishable. This means that one can go continuously from the metal to the ‘insulator’, suggesting that they might be the same phase.

On the Existence of Roton Excitations in Bose–Einstein Condensates: Signature of Proximity to a Mott Insulating Phase

Within the last decade, artificially engineered Bose–Einstein condensation has been achieved in atomic systems, Bose–Einstein Condensates (BECs) are superfluids just like bosonic helium is and all interacting bosonic fluids are expected to be at low enough temperatures. One difference between the two systems is that superfluid helium exhibits roton excitations while Bose–Einstein condensates have never been observed to have such excitations. The reason for the roton minimum in helium is its proximity to a solid phase. The roton minimum is a consequence of enhanced density fluctuations at the reciprocal lattice vector of the stillborn solid. Bose–Einstein condensates in atomic traps are not near a solid phase and therefore do not exhibit roton minimum. We conclude that if Bose–Einstein condensates in an optical lattice are tuned near a transition to a Mott insulating phase, a roton minimum will develop at a reciprocal lattice vector of the lattice. Equivalently, a peak in the structure factor will appear at such a wavevector. The smallness of the roton gap or the largeness of the structure factor peak are experimental signatures of the proximity to the Mott transition.

Topological excitations and their contribution to quantum criticality in 2+1 D antiferromagnets

Abstract It has been proposed that there are new degrees of freedom intrinsic to quantum critical points that contribute to quantum critical physics. We study 2 + 1 D antiferromagnets in order to explore possible new quantum critical physics arising from nontrivial topological effects. We show that skyrmion excitations are stable at criticality and have nonzero probability at arbitrarily low temperatures. To include quantum critical skyrmion effects, we find a class of exact solutions composed of skyrmion and antiskyrmion superpositions, which we call topolons. We include the topolons in the partition function and renormalize by integrating out small size topolons and short wavelength spin waves. We obtain a correlation length critical exponent ν = 0.9297 and anomalous dimension η = 0.3381 .

ON SUPERFLUIDITY AND SUPPRESSED LIGHT SCATTERING IN BECs

We show that the suppression of light scattering off a Bose Einstein Condensate is equivalent to the Landau argument for superfluidity and thus is a consequence of the Principle of Superfluidity. The superfluid ground state of a BEC contains nonseparable, nontrivial correlations between the bosons that make up the system, i.e., it is entangled. The correlations in the ground state entangle the bosons into a coherent state for the lowest energy state. The entanglement is so extreme that the bosons that make up the system cannot be excited at long wavenumbers. Their existence at low energies is impossible. Only quantum sound can be excited, i.e. the excitations are Bogolyubov quasiparticles which do not resemble free bosons whatsoever at low energies. This means that the system is superfluid by the Landau argument and the superfluidity is ultimately the reason for suppressed scattering at low wavelengths.

Mott transitions and phases in quantum bosonic solids and bosonic superfluids

We review the nature of superfluid ground states and the universality of their properties with emphasis to the Bose Einstein condensate (BEC) systems in atomic physics. We then study the superfluid Mott transition in such systems. We find that there could be two types of Mott transitions and phases. One of them was described long ago and corresponds to the suppression of Josephson tunneling within superfluids sitting at each well. On the other hand, the conditions of optical lattice BEC experiments are such that either the coherence length is longer than the interwell separation, or there is too small a number of bosons per well. This vitiates the existence of a superfluid order parameter within a well, and therefore of Josephson tunneling between wells. Under such conditions, there is a transition to a Mott phase which corresponds to the suppression of individual boson tunneling among wells. This last transition is in general discontinuous and can happen for incommensurate values of bosons per site. If the coherence length is small enough and the number of bosons per site is large enough, the transition studied in the earlier work will happen.