Imaginary-time replica formalism study of a quantum sphericalp-spin-glass model

Quantum Biroli-Mézard model: Glass transition and superfluidity in a quantum lattice glass model

“…This has been well established in the classical case [46]. In the quantum case, it has been studied in [29,30] for the imaginary time dynamics and in [50,51] for the real time dynamics. An heuristic argument that relates the transition in the real and imaginary time dynamics has been proposed in [9].…”

Dynamical study of the disordered quantump=2spherical model

“…To date, the introduction of quantum fluctuations in theoretical glassy models has not led to qualitative changes, e.g., new slow quantum modes, in their long-time dynamics [1,2,3,4,5]. Quantum fluctuations often drive the glass transition to be first-order [6,7,8,9,10], and thus only qualitatively affect the dynamical behavior on short-time scales. However there are examples where, in the absence of dissipation, quantum fluctuations lead to a quantum critical point at zero temperature; examples include the periodic Josephson array [11] and infinite-component quantum rotors [12,13].…”

Low-temperature specific heat of some quantum mean-field glassy phases

“…We consider a quantum extension of the spherical pspin glass model as studied in 7 , an interacting system of N continuous spins s i , 1 < i < N . This quantum extension consists in considering a continuous spin s i as an operator associated to a spatial coordinate and introducing its conjugated momentum π i which satisfies standard commutation relations…”

“…We also introduce the parameter Γ = 2 /(MJ), which measures the strength of quantum fluctuations. The phase diagram of (14) in the Γ − T plane was found 7 to be characterized by a line Γ c (T ) separating a paramagnetic (PM), associated to a diagonal matrix Q ab (τ ) = q d (τ )δ ab , from a spin-glass (SG) phase at low T , which we focus on here. The saddle point equations describing this SG phase is solved by a one step RSB ansatz 7 , shown to be exact as in the classical case, such that q(u) = 0 for u < m and q(u) = q EA for u > m, m being the breakpoint.…”

“…The saddle point equations describing this SG phase is solved by a one step RSB ansatz 7 , shown to be exact as in the classical case, such that q(u) = 0 for u < m and q(u) = q EA for u > m, m being the breakpoint. The internal energy, as a function of the saddle point solution is given by 7 : (18) with the saddle point equations…”