Sine-Gordon/Coulomb Gas Soliton Correlation Functions and an Exact Evaluation of the Kosterlitz--Thouless Critical Exponent

Mondaini, Leonardo; Marino, E. C.

doi:10.1007/s10955-004-8828-y

Cited by 8 publications

(13 citation statements)

References 24 publications

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“…The power‐law behavior of the skyrmion (vortex) correlation functions is precisely the one found in a BKT phase 5, 9 and therefore the BKT mechanism stabilizes the SG phase in this system, even at a finite temperature.…”

Section: Skyrmion Correlation Functionssupporting

confidence: 57%

Quantum skyrmions and the stability of an SO(3) quantum spin‐glass

Marino

Conceição

2010

Physica Status Solidi (b)

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We explore the order-disorder duality relation existing between the spin degrees of freedom and the skyrmion topological excitations in a quenched, disordered SO(3) quantum spin system described by a Heisenberg hamiltonian with nearest neighbor interactions and a Gaussian distribution of couplings. The quantum skyrmion correlation functions are evaluated in each of the phases presented by the system. These realize all possibilities allowed by the duality relation. There is a spinglass phase at finite temperature, where the skyrmion correlator have a power-law behavior. The Berezinskii-KosterlitzThouless (BKT) mechanism stabilizes this phase. 1 Introduction Many physical systems contain in their spectrum, the so-called topological excitations. These bear observable quantities whose conservation does not follow from the existence of any continuum symmetries; rather it is a consequence of the nontrivial topology of the configuration space. The quantization of such excitations requires specific methods, since they are usually not simply related to degrees of freedom appearing in the hamiltonian. One interesting feature of these excitations is that they work as disorder parameters for a given system [1]. This generates a duality relation between the topological and hamiltonian excitations creation operators, which has been exploited in order to derive a general method for evaluating the correlation functions of topological excitations [2].In this work, we apply this method in order to describe the quantum skyrmions of a two-dimensional spin-glass (SG) system, which has been studied recently [3,4] and which presents three phases: paramagnetic (PM), Néel, and SG. We show that in the latter the skyrmions (vortices in the CP 1 field theory framework) have a power-law behavior, thereby revealing that the Berezinskii-Kosterlitz-Thouless (BKT) mechanism [5] is the one responsible for stabilizing this phase.

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Section: Skyrmion Correlation Functionssupporting

confidence: 57%

Quantum skyrmions and the stability of an SO(3) quantum spin‐glass

Marino

Conceição

2010

Physica Status Solidi (b)

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“…In this work we employ the same methodology established in [1] to compute the two-point fermion correlation functions of the MTM, which, as is well-known, is also connected to the SG theory [5]. The MTM and the associated SG theory, indeed, are some of the best studied quantum field theories.…”

Section: Introductionmentioning

confidence: 99%

Exact asymptotic behaviour of fermion correlation functions in the massive Thirring model

Mondaini¹,

Marino²

2006

J. Phys. A: Math. Gen.

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Abstract. We obtain an exact asymptotic expression for the two-point fermion correlation functions in the massive Thirring model (MTM) and show that, for β 2 = 8π, they reproduce the exactly known corresponding functions of the massless theory, explicitly confirming the irrelevance of the mass term at this point. This result is obtained by using the Coulomb gas representation of the fermionic MTM correlators in the bipolar coordinate system.

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“…( 10) implies that the operator µ creates eigenstates of the topological charge Q, with eigenvalue 2π/N, thus proving that the quantum solitons occurring in the theory described by ( 1) are indeed phase solitons. Correlation functions of these quantum soliton excitations have been calculated elsewhere [10,11,12]. In Section 4, we will show that the relevant quantum correlators for the calculation of the conductivity will be the soliton current-current correlators.…”

Section: Quantum Phase Solitons In Theories With a Z(n) Symmetrymentioning

confidence: 99%

Vanishing conductivity of quantum solitons in polyacetylene

Mondaini¹,

Marino²,

Schmidt³

2009

J. Phys. A: Math. Theor.

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Quantum solitons or polarons are supposed to play a crucial role in the electric conductivity of polyacetylene, in the intermediate doping regime. We present an exact fully quantized calculation of the quantum soliton conductivity in polyacetylene and show that it vanishes exactly. This is obtained by applying a general method of soliton quantization, based on order-disorder duality, to a Z(2)-symmetric complex extension of the TLM dimerization effective field theory. We show that, in this theory, polyacetylene solitons are sine-Gordon solitons in the phase of the complex field.

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Sine-Gordon/Coulomb Gas Soliton Correlation Functions and an Exact Evaluation of the Kosterlitz--Thouless Critical Exponent

Cited by 8 publications

References 24 publications

Quantum skyrmions and the stability of an SO(3) quantum spin‐glass

Quantum skyrmions and the stability of an SO(3) quantum spin‐glass

Exact asymptotic behaviour of fermion correlation functions in the massive Thirring model

Vanishing conductivity of quantum solitons in polyacetylene

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