Periodic instanton and phase transition in quantum tunneling of spin systems

Zhang, Yunbo; Nie, Yi-Hang; Kou, Su-Peng; Liang, J.-Q.; Müller-Kirsten, Harald J W; Pu, Fu‐Cho

doi:10.1016/s0375-9601(99)00044-4

Cited by 7 publications

(13 citation statements)

References 23 publications

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“…Consider the following Euclidean action for onedimensional quantum models (in dimensionless unity) [13][14][15]:…”

Section: Periodons and Transitions In Quantum Tunnelingmentioning

confidence: 99%

“…In the specific context of condensed matter Physics, the role of instantons in tunneling processes observed a e-mail: fernand.naha.nz@gmail.com b e-mail: dikande.alain@ubuea.cm (corresponding author) c e-mail: esmkam@yahoo.com in some of these systems at low temperatures is now well established [11][12][13][14]. As a matter of fact, in multistate systems, the transitions between two states separated by an energy barrier usually occur either in the classical regime, where they are driven by thermal activations, or in the quantum regime driven by tunneling processes.…”

Section: Introductionmentioning

confidence: 99%

“…However, as the temperature approaches zero, quantum fluctuations gain in importance and the transition is driven by quantum tunnelings through the barrier. However in the later case, the system dynamics can be described by classical configurations which are either instantons or vacuum, that dominate the thermal rate [11][12][13][14][15]. As the temperature increases, thermally-induced crossovers become more and more relevant and at some critical temperature a phase transition in quantum tunneling can take place [13][14][15].…”

Section: Introductionmentioning

confidence: 99%

“…However in the later case, the system dynamics can be described by classical configurations which are either instantons or vacuum, that dominate the thermal rate [11][12][13][14][15]. As the temperature increases, thermally-induced crossovers become more and more relevant and at some critical temperature a phase transition in quantum tunneling can take place [13][14][15]. The phenomenon of phase transition in quantum tunneling has been extensively investigated over the past years [13][14][15]; thus, it is known that some physical systems can exhibit not only a smooth second-order transition in quantum tunneling at a critical temperature T (2) 0 , but a transition of the first order can also occur [13,[16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

“…As the temperature increases, thermally-induced crossovers become more and more relevant and at some critical temperature a phase transition in quantum tunneling can take place [13][14][15]. The phenomenon of phase transition in quantum tunneling has been extensively investigated over the past years [13][14][15]; thus, it is known that some physical systems can exhibit not only a smooth second-order transition in quantum tunneling at a critical temperature T (2) 0 , but a transition of the first order can also occur [13,[16][17][18][19][20][21]. Instructively, this first-order transition in quantum tunneling is closely related to the variation of the instanton action with respect to the instanton energy [13,[16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

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Quantum-tunneling transitions and exact statistical mechanics of bistable systems with parametrized Dikandé–Kofané double-well potentials

2022

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We consider a one-dimensional system of interacting particles (which can be atoms, molecules, ions, etc.), in which particles are subjected to a bistable potential the double-well shape of which is tunable via a shape deformability parameter. Our objective is to examine the impact of shape deformability on the order of transition in quantum tunneling in the bistable system, and on the possible existence of exact solutions to the transfer-integral operator associated with the partition function of the system. The bistable potential is represented by a class composed of three families of parametrized double-well potentials, whose minima and barrier height can be tuned distinctly. It is found that the extra degree of freedom, introduced by the shape deformability parameter, favors a first-order transition in quantum tunneling, in addition to the second-order transition predicted with the $$\phi ^4$$ ϕ 4 model. This first-order transition in quantum tunneling, which is consistent with Chudnovsky’s conjecture of the influence of the shape of the potential barrier on the order of thermally assisted transitions in bistable systems, is shown to occur at a critical value of the shape-deformability parameter which is the same for the three families of parametrized double-well potentials. Concerning the statistical mechanics of the system, the associate partition function is mapped onto a spectral problem by means of the transfer-integral formalism. The condition that the partition function can be exactly integrable, is determined by a criterion enabling exact eigenvalues and eigenfunctions for the transfer-integral operator. Analytical expressions of some of these exact eigenvalues and eigenfunctions are given, and the corresponding ground-state wavefunctions are used to compute the probability density which is relevant for calculations of thermodynamic quantities such as the correlation functions and the correlation lengths. Graphic Abstract

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“…Consider the following Euclidean action for onedimensional quantum models (in dimensionless unity) [13][14][15]:…”

Section: Periodons and Transitions In Quantum Tunnelingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantum-tunneling transitions and exact statistical mechanics of bistable systems with parametrized Dikandé–Kofané double-well potentials

2022

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Macroscopic quantum tunneling and quantum–classical phase transitions of the escape rate in large spin systems

Owerre

Paranjape

2015

Physics Reports

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This article presents a review on the theoretical and the experimental developments on macroscopic quantum tunneling and quantum-classical phase transitions of the escape rate in large spin systems. A substantial amount of research work has been done in this area of research over the years, so this article does not cover all the research areas that have been studied, for instance the effect of dissipation is not discussed and can be found in other review articles. We present the basic ideas with simplified calculations so that it is readable to both specialists and nonspecialists in this area of research. A brief derivation of the path integral formulation of quantum mechanics in its original form using the orthonormal position and momentum basis is reviewed. For tunneling of a particle into the classically forbidden region, the imaginary time (Euclidean) formulation of path integral is useful, we review this formulation and apply it to the problem of tunneling in a double well potential. For spin systems such as single molecule magnets, the formulation of path integral requires the use of non-orthonormal spin coherent states in (2s + 1) dimensional Hilbert space, the coordinate independent and the coordinate dependent form of the spin coherent state path integral are derived. These two (equivalent) forms of spin coherent state path integral are applied to the tunneling of single molecule magnets through a magnetic anisotropy barrier. Most experimental and numerical results are presented. The suppression of tunneling for half-odd integer spin (spin-parity effect) at zero magnetic field is derived using both forms of spin coherent state path integral, which shows that this result (spin-parity effect) is independent of the choice of coordinate. At nonzero magnetic field we present both the experimental and the theoretical results of the oscillation of tunneling splitting as a function of the applied magnetic field applied along the spin hard anisotropy axis direction. The experimental and the theoretical results of the tunneling in antiferromagnetic exchange coupled dimer model are also reviewed. As the spin coherent state path integral formalism is a semi-classical method, an alternative exact mapping of a spin Hamiltonian to a particle Hamiltonian with a potential field (effective potential method) is derived. This effective potential method allows for the investigation of quantum-classical phase transitions of the escape rate in large spin systems. We present different methods for investigating quantum-classical phase transitions of the escape rate in large spin systems. These methods are applied to different spin models.PACS numbers: 75.45.+j, 75.50.Tt, 75.30.Gw, 03.65.Sq,75.10.Jm, 75.60.Ej, 61.46.+w linear superposition of the classical ground states with an energy splitting between them (Coleman, 1985;Landau and Lifshitz, 1977). In some cases the two minima of the potential are not degenerate. The state with lower energy is the true vacuum, while the state with higher energy is the false vacuum, which is th...

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Basic and Fluctuating Periodic Instantons in Quantum Tunneling

Shi-Kuo¹,

Fu²,

Liu³

et al. 2016

Commun. Theor. Phys.

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Under condition of four potential fields, equations of motion and fluctuations in imaginary time are utilized to analytically derive the basic and fluctuating periodic instantons. It is shown that the basic instantons satisfy the elliptic or simple pendulum equations and their solutions are Jacobi elliptic functions, and fluctuating periodic instantons satisfy the Lamé equation and their solutions are Lamé functions. These results indicate that there exists the common solution family for different potential fields which are called the super-symmetry family.

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Periodic instanton and phase transition in quantum tunneling of spin systems

Cited by 7 publications

References 23 publications

Quantum-tunneling transitions and exact statistical mechanics of bistable systems with parametrized Dikandé–Kofané double-well potentials

Quantum-tunneling transitions and exact statistical mechanics of bistable systems with parametrized Dikandé–Kofané double-well potentials

Macroscopic quantum tunneling and quantum–classical phase transitions of the escape rate in large spin systems

Basic and Fluctuating Periodic Instantons in Quantum Tunneling

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