Systems with Symmetry Breaking and Restoration

Statistical systems, in which spontaneous symmetry breaking can be accompanied by spontaneous local symmetry restoration, are considered. A general approach to describing such systems is formulated, based on the notion of weighted Hilbert spaces and configuration averaging. The approach is illustrated by the example of a ferroelectric with mesoscopic fluctuations of paraelectric phase. The influence of the local symmetry restoration on the system characteristics, such as sound velocity and Debye-Waller factor, is discussed.Comment: Latex file, 32 page

Symmetry breaking and quantum correlations in finite systems: Studies of quantum dots and ultracold Bose gases and related nuclear and chemical methods

Investigations of emergent symmetry breaking phenomena occurring in small finite-size systems are reviewed, with a focus on the strongly correlated regime of electrons in two-dimensional semicoductor quantum dots and trapped ultracold bosonic atoms in harmonic traps. Throughout the review we emphasize universal aspects and similarities of symmetry breaking found in these systems, as well as in more traditional fields like nuclear physics and quantum chemistry, which are characterized by very different interparticle forces. A unified description of strongly correlated phenomena in finite systems of repelling particles (whether fermions or bosons) is presented through the development of a two-step method of symmetry breaking at the unrestricted Hartree-Fock level and of subsequent symmetry restoration via post Hartree-Fock projection techniques. Quantitative and qualitative aspects of the two-step method are treated and validated by exact diagonalization calculations. Strongly-correlated phenomena emerging from symmetry breaking include: (I) Chemical bonding, dissociation, and entanglement (at zero and finite magnetic fields) in quantum dot molecules and in pinned electron molecular dimers formed within a single anisotropic quantum dot. (II) Electron crystallization, with particle localization on the vertices of concentric polygonal rings, and formation of rotating electron molecules (REMs) in circular quantum dots. (III) At high magnetic fields, the REMs are described by parameter-free analytic wave functions, which are an alternative to the Laughlin and composite-fermion approaches. (IV) Crystalline phases of strongly repelling bosons. In rotating traps and in analogy with the REMs, such repelling bosons form rotating boson molecules (RBMs).Comment: Review article published in Reports on Progress in Physics. REVTEX4. 95 pages with 37 color figures. To download a copy with high-quality figures, go to publication #82 in http://www.prism.gatech.edu/~ph274cy

Symmetry breaking/symmetry preserving circuits and symmetry restoration on quantum computers: A quantum many-body perspective

We discuss here some aspects related to symmetries of a quantum many-body problem when trying to treat it on a quantum computer. Several features related to symmetry conservation, symmetry breaking and possible symmetry restoration are reviewed. After a brief discussion of some of the standard symmetries relevant for many-particle systems, we discuss the advantage to encode directly some symmetries in quantum ansatze, especially with the aim to reduce the quantum register size. It is however well-known that the use of symmetry breaking states can also be a unique way to incorporate specific internal correlations when a spontaneous symmetry breaking occurs. These aspects are discussed in the quantum computing context. Precise description of quantum systems can however be achieved only when the symmetries that are initially broken are properly restored. Several methods are introduced to perform symmetry restoration on a quantum computer, for instance, purification of the state by means of the Grover algorithm, use of the combination of Hadamard test and oracle concepts, symmetry filtering by quantum phase estimation and by an iterative independent set of Hadamard tests.Comment: submitted to Eur. Phys. J. A in the topical issue on "Quantum computing in low-energy nuclear theory

Atomic Quantum Simulation of U(N) and SU(N) Non-Abelian Lattice Gauge Theories

Using ultracold alkaline-earth atoms in optical lattices, we construct a quantum simulator for U(N) and SU(N) lattice gauge theories with fermionic matter based on quantum link models. These systems share qualitative features with QCD, including chiral symmetry breaking and restoration at non-zero temperature or baryon density. Unlike classical simulations, a quantum simulator does not suffer from sign problems and can address the corresponding chiral dynamics in real time.Comment: 12 pages, 5 figures. Main text plus one basic introduction to the topic and one supplementary material on implementation. Final versio

Chiral phase transitions and quantum critical points of the D3/D7(D5) system with mutually perpendicular E and B fields at finite temperature and density

We study chiral symmetry restoration with increasing temperature and density in gauge theories subject to mutually perpendicular electric and magnetic fields using holography. We determine the chiral symmetry breaking phase structure of the D3/D7 and D3/D5 systems in the temperature-density-electric field directions. A magnetic field may break the chiral symmetry and an additional electric field induces Ohm and Hall currents as well as restoring the chiral symmetry. At zero temperature the D3/D5 system displays a line of holographic BKT phase transitions in the density-electric field plane, while the D3/D7 system shows a mean-field phase transition. At intermediate temperatures, the transitions in the density-electric field plane are of first order at low density, transforming to second order at critical points as density rises. At high temperature the transition is only ever first order.Comment: 15 pages, 7 figures, v2: Added a referenc

Defect mediated melting and the breaking of quantum double symmetries

In this paper, we apply the method of breaking quantum double symmetries to some cases of defect mediated melting. The formalism allows for a systematic classification of possible defect condensates and the subsequent confinement and/or liberation of other degrees of freedom. We also show that the breaking of a double symmetry may well involve a (partial) restoration of an original symmetry. A detailed analysis of a number of simple but representative examples is given, where we focus on systems with global internal and external (space) symmetries. We start by rephrasing some of the well known cases involving an Abelian defect condensate, such as the Kosterlitz-Thouless transition and one-dimensional melting, in our language. Then we proceed to the non-Abelian case of a hexagonal crystal, where the hexatic phase is realized if translational defects condense in a particular rotationally invariant state. Other conceivable phases are also described in our framework.Comment: 10 pages, 4 figures, updated reference