Dynamic polarizability of an exactly solvable model of diatomic molecule

Summary A very simple one-dimensional model for a one-electron diatomic molecule under the agency of a homogeneous, time-dependent electric field is investigated in the linear-response approximation. The behaviour of the dynamic polarizability is studied as a function of the frequency ω and the internuclear separationR.

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Riassunto Nell'approssimazione della risposta lineare si studia l'influenza di un (debole) campo elettrico dipendente dal tempo su un semplice modello monodimensionale di molecola biatomica omonucleare contenente un unico elettrone ?attivo?. Si studia la dipendenza della polarizzabilità dinamica dalla frequenza ω e dalla distanza internucleareR.

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Резюме В приближении линейного отклика рассматривается очень простая одномерная модель для одноэлектронной двухатомной молекулы при наличии (слабого) электрического поля, зависящего от времени. Исследуется поведение динамической поляризуемости, как функции частоты ω и расстояния между ядрамиR.

     

Homological stabilizer codes

In this paper we define homological stabilizer codes on qubits which encompass codes such as Kitaev’s toric code and the topological color codes. These codes are defined solely by the graphs they reside on. This feature allows us to use properties of topological graph theory to determine the graphs which are suitable as homological stabilizer codes. We then show that all toric codes are equivalent to homological stabilizer codes on 4-valent graphs. We show that the topological color codes and toric codes correspond to two distinct classes of graphs. We define the notion of label set equivalencies and show that under a small set of constraints the only homological stabilizer codes without local logical operators are equivalent to Kitaev’s toric code or to the topological color codes.     

Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes

Searches for possible new quantum phases and classifications of quantum phases have been central problems in physics. Yet, they are indeed challenging problems due to the computational difficulties in analyzing quantum many-body systems and the lack of a general framework for classifications. While frustration-free Hamiltonians, which appear as fixed point Hamiltonians of renormalization group transformations, may serve as representatives of quantum phases, it is still difficult to analyze and classify quantum phases of arbitrary frustration-free Hamiltonians exhaustively. Here, we address these problems by sharpening our considerations to a certain subclass of frustration-free Hamiltonians, called stabilizer Hamiltonians, which have been actively studied in quantum information science. We propose a model of frustration-free Hamiltonians which covers a large class of physically realistic stabilizer Hamiltonians, constrained to only three physical conditions; the locality of interaction terms, translation symmetries and scale symmetries, meaning that the number of ground states does not grow with the system size. We show that quantum phases arising in two-dimensional models can be classified exactly through certain quantum coding theoretical operators, called logical operators, by proving that two models with topologically distinct shapes of logical operators are always separated by quantum phase transitions.     

Heat flow in an exactly solvable model

A chain of one-dimensional oscillators is considered. They are mechanically uncoupled and interact via a stochastic process which redistributes the energy between nearest neighbors. The total energy is kept constant except for the interactions of the extremal oscillators with reservoirs at different temperatures. The stationary measures are obtained when the chain is finite; the thermodynamic limit is then considered, approach to the Gibbs distribution is proven, and a linear temperature profile is obtained.     

Correlation functions in an exactly solvable tefface-ledge-kink model

We solve exactly a terrace-ledge-kink (TLK) model describing a vicinal section of a crystal surface at a microscopic level, with either repulsive or attractive interactions between the ledges. As expected there is a faceting, or reconstructive, phase transition, driven either by temperature or by the chemical potential, that controls the mean slope of the surface. In the rough phase we carry out a thorough investigation of microscopic thermal fluctuations of the interface. This is done by combining Bethe ansatz and Conformal Field Theory methods in order to calculate appropriately defined correlators.     

The reduced α-amplitude in an exactly solvable model

In recent work by Fliessbach the removal of an α-particle from a nucleus under the influence of a perturbation was considered. Using certain approximations the many-body transition matrix element was reduced to a one-body matrix element. This one-body matrix element showed that the appropriate bound α-amplitude in the initial nucleus (reduced amplitude) depends on the energy transferred to the removed α-particle. The present paper deals with an analytic model in which the one-body transition matrix element as given in that work can be derived exactly from the original microscopic matrix element.     

凝聚体中的拓扑量子态

探寻拓扑上非平庸的凝聚体物质状态,特别是其电子结构和输运性质,是当前凝聚体物理 学领域非常重要的前沿研究方向。本文讨论的大多数主题都与电子波函数的拓扑性质有关。全文 除简短的引言外,包括拓扑量子现象、各种拓扑相、拓扑性准粒子的异常输运性质、拓扑性集 体激发和耦合激发,以及继续发展的拓扑量子态研究五个章节。这些章节着重反映拓扑量子态研 究的各个侧面,汇总起来方可以凸显凝聚体中拓扑量子态的全貌。     

A short and efficient error correcting code for polarization coded photonic qubits in a dissipative channel

We propose a short and efficient non-degenerate quantum error correcting code that is adapted for qubits encoded on two orthogonal, single-photon states (e.g., horizontally and vertically polarized) subject to a dissipative channel.The proposed code draws its strength from the fact that it is adapted to the physical characteristics of the information-carrying basis states under the action of the channel. The code combines different energy manifolds and consists of only 3 spatio-temporal modes and on average 2 photons per code word.     

Distribution of pore-size in an exactly solvable two-dimensional biomembrane model

A model for a two-dimensional lipid bilayer in which both short range repulsive forces and long range attractive forces play a role, and which can be solved exactly, is discussed. It is shown that the bilayer consists of long stretches of relatively densely packed lipids separated by small pores. The statistical distributions of number and size of the pores are calculated from first principles.     

Fluctuation effects in an exactly solvable model of phase transitions

An investigation is made of an exactly solvable phase transition model, which takes account of interaction only between fluctuations with equal and antiparallel momenta. It is shown that within this model fluctuation-induced first-order phase transitions are possible in agreement with renormalization group analysis predictions. The model is generalized phenomenologically, which leads to correct values of all large critical exponents. The effect of frozen-in impurities on a phase transition is studied and it is shown that in a narrow range proportional to the impurity concentration the phase transition smears.     

Negative-parity bands and gapless superconductivity in an exactly solvable model

In addition to the positive-parity yrast states discussed previously, exact solutions of the R(8) (two-level) model are found, interpretable as negative-parity yrast states. Similar solutions for the three- and four-level models are also considered. These are of special interest in connection with the phenomenon of gapless superconductivity. The states in question usually originate from two-quasiparticle rotational bands, but for some values of the spin, four- and six-quasi-particle bands may become “yrast.” With exact solutions available, the self-consistent cranking approximation is tested on these excited bands.     

Feasibility of self-correcting quantum memory and thermal stability of topological order

Recently, it has become apparent that the thermal stability of topologically ordered systems at finite temperature, as discussed in condensed matter physics, can be studied by addressing the feasibility of self-correcting quantum memory, as discussed in quantum information science. Here, with this correspondence in mind, we propose a model of quantum codes that may cover a large class of physically realizable quantum memory. The model is supported by a certain class of gapped spin Hamiltonians, called stabilizer Hamiltonians, with translation symmetries and a small number of ground states that does not grow with the system size. We show that the model does not work as self-correcting quantum memory due to a certain topological constraint on geometric shapes of its logical operators. This quantum coding theoretical result implies that systems covered or approximated by the model cannot have thermally stable topological order, meaning that systems cannot be stable against both thermal fluctuations and local perturbations simultaneously in two and three spatial dimensions.     

Long-range order in the XXZ model

The existence of long-range order is proved under certain conditions for the antiferromagnetic quantum spin system with anisotropic interactions (XXZ model) on the simple cubic or the square lattice. In three dimensions (the simple cubic lattice), finite long-range order exists at sufficiently low temperatures for any anisotropy(0) ifS1, and for 0<0.29 (XY-like) or>1.19 (Ising-like) ifS=1/2. In two dimensions (the square lattice), ground-state long-range order exists under the following conditions: for any anisotropy (0) ifS3/2; 0<0.032 (XY-like) or 0.67<<1.34 (almost isotropic) or>1.80 (Ising-like) ifS=1;>1.93 (Ising-like) ifS=1/2. We conjecture that the two-dimensional spin-1/2XY model (=0) has finite ground-state long-range order. Numerical evidence supporting this conjecture is given.     

On the wave functions of an exactly solvable model of interacting fermions with spin 1/2 in an external field

It is shown that hyperbolic systems of Sutherland spin 1/2 particles in an external field with the Morse potential characterized by parameter τ² have a discrete part of their spectrum in the case of a particular constraint on the τ, parameter of two-particle interaction λ, and the number of particles. The ground state is described by a Jastrow wave function. The results known for systems with an interaction inversely proportional to the squared distance between particles are reproduced in the limit τ → ∞.     

Fractional statistics in one dimension: view from an exactly solvable model

One-dimensional fractional statistics is studied using the Calogero-Sutherland model (CSM) which describes a system of non-relativistic quantum particles interacting with an inverse-square two-body potential on a ring. The inverse-square exchange can be regarded as a pure statistical interaction and this system can be mapped to an ideal gas obeying the fractional exclusion and exchange statistics. The details of the exact calculations of the dynamical correlation functions or this ideal system is presented in this paper. An effective low-energy one-dimensional “anyon” model is constructed; and its correlation functions are found to be in agreement with those in the CSM; and this agreement provides an evidence for the equivalence of the first- and the second-quantized construction of the 1D anyon model at least in the long-wavelength limit. Furthermore, the finite-size scaling applicable to the conformally invariant systems is used to obtain the complete set of correlation exponents for the CSM.     

Test of the many-electron theory of atoms in an exactly solvable model

The many-electron theory of ground states of Sinano?lu is tested on an exactly solvable model. The many electron theory wave functions and energies reproduce closely the exact solutions.     

Twist in an exactly solvable directed lattice ribbon

We investigate the transition between a twisted regime and a disordered regime in a directed ribbon model on a cubic lattice. A fugacity corresponding to an interaction which models half-twists in the ribbon is introduced and the interacting model is solved exactly. Our results suggest that conformational entropy and a local interaction which induces twist are key ingredients to model qualitatively the crossover behavior between a twisted (helical) regime and a denatured regime in duplex biopolymers such as DNA.