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We study the role of particle-hole symmetry on the universality class of various quantum phase transitions corresponding to the onset of superfluidity at zero temperature of bosons in a quenched random medium. The functional integral formulation of this problem in d spatial dimensions yields a (d+1)-dimensional classical XY-model with extended disorder--the so-called random rod problem. Particle-hole symmetry may then be broken by adding nonzero site energies. We may distinguish three cases: (i) exact particle-hole symmetry, in which the site energies all vanish, (ii) statistical particle-hole symmetry in which the site energy distribution is symmetric about zero, vanishing on average, and (iii) complete absence of particle-hole symmetry in which the distribution is generic. We explore in each case the nature of the excitations in the non-superfluid Mott insulating and Bose glass phases. We find that the Bose glass compressibility, which has the interpretation of a temporal spin stiffness or superfluid density, is positive in cases (ii) and (iii), but that it vanishes with an essential singularity as full particle-hole symmetry is restored. We then focus on the critical point and discuss the relevance of type (ii) particle-hole symmetry breaking perturbations to the random rod critical behavior. We argue that a perturbation of type (iii) is irrelevant to the resulting type (ii) critical behavior: the statistical symmetry is restored on large scales close to the critical point, and case (ii) therefore describes the dirty boson fixed point. To study higher dimensions we attempt, with partial success, to generalize the Dorogovtsev-Cardy-Boyanovsky double epsilon expansion technique to this problem. The qualitative renormalization group flow picture this technique provides is quite compelling.
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It is shown that previous arguments leading to the equality $z=d$ ($d$ being the spatial dimensionality) for the dynamical exponent describing the Bose glass to superfluid transition may break down, as apparently seen in recent simulations (Ref. cite{Baranger}). The key observation is that the major contribution to the compressibility, which remains finite through the transition and was predicted to scale as $kappa sim |delta|^{(d-z) u}$ (where $delta$ is the deviation from criticality and $ u$ is the correlation length exponent) comes from the analytic part, not the singular part of the free energy, and therefore is not restricted by any conventional scaling hypothesis.
We study quantum transport in disordered systems with particle-hole symmetric Hamiltonians. The particle-hole symmetry is spontaneously broken after averaging with respect to disorder, and the resulting massless mode is treated in a random-phase representation of the invariant measure of the symmetry-group. We compute the resulting fermionic functional integral of the average two-particle Greens function in a perturbation theory around the diffusive limit. The results up to two-loop order show that the corrections vanish, indicating that the diffusive quantum transport is robust. On the other hand, the diffusion coefficient depends strongly on the particle-hole symmetric Hamiltonian we choose to study. This reveals a connection between the underlying microscopic theory and the classical long-scale metallic behaviour of these systems.
In this work we probe the dynamics of the particle-hole symmetric many-body localized (MBL) phase. We provide numerical evidence that it can be characterized by an algebraic propagation of both entanglement and charge, unlike in the conventional MBL case. We explain the mechanism of this anomalous diffusion through a formation of bound states, which coherently propagate via long-range resonances. By projecting onto the two-particle sector of the particle-hole symmetric model, we show that the formation and observed subdiffusive dynamics is a consequence of an interplay between symmetry and interactions.
We show that a {em vibrational instability} of the spectrum of weakly interacting quasi-local harmonic modes creates the maximum in the inelastic scattering intensity in glasses, the Boson peak. The instability, limited by anharmonicity, causes a complete reconstruction of the vibrational density of states (DOS) below some frequency $omega_c$, proportional to the strength of interaction. The DOS of the new {em harmonic modes} is independent of the actual value of the anharmonicity. It is a universal function of frequency depending on a single parameter -- the Boson peak frequency, $omega_b$ which is a function of interaction strength. The excess of the DOS over the Debye value is $proptoomega^4$ at low frequencies and linear in $omega$ in the interval $omega_b ll omega ll omega_c$. Our results are in an excellent agreement with recent experimental studies.
We study the scaling properties of the solid-on-solid front of the infinite cluster in two-dimensional gradient percolation. We show that such an object is self affine with a Hurst exponent equal to 2/3 up to a cutoff-length proportional to the gradient to the power (-4/7). Beyond this length scale, the front position has the character of uncorrelated noise. Importantly, the self-affine behavior is robust even after removing local jumps of the front. The previously observed multi affinity, is due to the dominance of overhangs at small distances in the structure function. This is a crossover effect.
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