Temperature Dependence of the Superconducting Gap in High-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>T</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math>Cuprates

Fine, Boris V.

doi:10.1103/physrevlett.94.157005

Cited by 8 publications

(2 citation statements)

References 20 publications

(24 reference statements)

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“…This model (or its close proxies) can describe bosons on a lattice with next-nearest hard-core constraints [25,9] or Rydberg atoms on a lattice subject to dipole blockade preventing simultaneous excitation of two neighboring atoms [16,2]. Furthermore, a onedimensional version of the two-fermion model of high-temperature superconductivity in cuprates [10,11,1] can be mapped to the Hamiltonian (1) in a certain limit. The three-body interaction in eq.…”

Section: Pxp Model and Its Integrals Of Motionmentioning

confidence: 99%

“…One can always choose numerical coefficients c i in such a way that I Σ has a nondegenerate spectrum. 5 The awkwardness of the functional dependence (11) is particularly stunning for a translation-invariant system of fermions with periodic boundary conditions. The Hamiltonian and the total momentum are two integrals of motion of this system, which are generally regarded as independent.…”

Section: Complexity Of Functional Dependencementioning

confidence: 99%

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A Remark on the Notion of Independence of Quantum Integrals of Motion in the Thermodynamic Limit

Lychkovskiy

2020

J Stat Phys

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Studies of integrable quantum many-body systems have a long history with an impressive record of success. However, surprisingly enough, an unambiguous definition of quantum integrability remains a matter of an ongoing debate. We contribute to this debate by dwelling upon an important aspect of quantum integrability -the notion of independence of quantum integrals of motion (QIMs). We point out that a widely accepted definition of functional independence of QIMs is flawed, and suggest a new definition. Our study is motivated by the PXP model -a model of N spins 1/2 possessing an extensive number of binary QIMs. The number of QIMs which are independent according to the common definition turns out to be equal to the number of spins, N . A common wisdom would then suggest that the system is completely integrable, which is not the case. We discuss the origin of this conundrum and demonstrate how it is resolved when a new definition of independence of QIMs is employed.Keywords Quantum integrability · Integrals of motion · Functional independence · PXP model 1 Introduction A classical Hamiltonian system with N degrees of freedom is said to be completely integrable if it posses N functionally independent integrals of motion in involution (i.e. with pairwise commuting Poisson brackets). This concise, clear and rigorous definition is a mainstay of the well-developed and very fruitful theory of classical integrability. The situation with quantum integrability is 2 Oleg Lychkovskiy remarkably different: It is fair to say that even a commonly accepted rigorous definition of quantum integrability is lacking. An attempt of a straightforward translation of the classical definition to the quantum language stumbles upon several ambiguities: How to define and count quantum "degrees of freedom" [35,32,8]? What notion of independence of quantum integrals of motion (QIMs) should be used [26,12,29]? Should proper integrals of motion be local in some sense [5]? While a number of working definitions of quantum integrability are in use [34,12,5,28,22,21], none of them is of the same level of rigor, generality and usefulness as the definition of the classical integrability. The very existence of several different definitions indicates that the issue is not settled.It is expected that integrable and non-integrable quantum many-body systems are markedly different in a number of aspects. The list of differences includes the (non)existence of an extensive number of local integrals of motion, level statistics (Wigner-Dyson [4] vs Poisson [3]), (non)validity of the eigenstate thermalization hypothesis [6,27,23,14] and the canonical universality hypothesis [7], the nature of the local steady state approached after relaxation from a non-equilibrium initial state (Gibbs thermal state vs generalized Gibbs state) [33,18]. These expectations are rooted in a huge amount of analytical and numerical work pertaining to specific systems as well as in insights from the random matrix theory [18]. This body of work shows that typically a system which possesse...

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Section: Pxp Model and Its Integrals Of Motionmentioning

confidence: 99%

Section: Complexity Of Functional Dependencementioning

confidence: 99%

A Remark on the Notion of Independence of Quantum Integrals of Motion in the Thermodynamic Limit

Lychkovskiy

2020

J Stat Phys

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Electronically Driven Superlattice in the Cuprates

Egami

2007

J Supercond Nov Magn

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Resistive studies of the pseudogap in YBCO films with consideration of the transition from BCS to Bose–Einstein condensation

Solovjov

Dmitriev

2006

Low Temperature Physics

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A new approach is proposed for analysis of the excess conductivity σ′(T) arising below a characteristic temperature T*⪢Tc in YBa2Cu3O7−y (YBCO) films with different oxygen concentrations. The approach is based on the idea that σ′(T) is formed as a result of the formation at T⩽T* of local pairs (tightly bound bosons) obeying Bose–Einstein statistics in the temperature interval Tm<T<T*. At temperatures Tcmf<T<Tm the pairs obey BCS theory (Tcmf is the critical temperature separating the phase transition region from the region of critical fluctuations). Thus in Y123 systems a transition from Bose–Einstein condensation to condensation of the BCS type occurs with decreasing temperature. An equation in which the dynamics of formation of the tightly bound bosons is taken into account is proposed which gives a good description of the temperature dependence σ′(T) and in which the parameter Δ*, identified with the pseudogap in high-Tc superconductors, is contained in explicit form. The temperature dependence Δ*(T) is obtained for all the films studied.

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Temperature Dependence of the Superconducting Gap in High-TcCuprates

Cited by 8 publications

References 20 publications

A Remark on the Notion of Independence of Quantum Integrals of Motion in the Thermodynamic Limit

A Remark on the Notion of Independence of Quantum Integrals of Motion in the Thermodynamic Limit

Electronically Driven Superlattice in the Cuprates

Resistive studies of the pseudogap in YBCO films with consideration of the transition from BCS to Bose–Einstein condensation

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