Finite-Size Scaling at First-Order Quantum Transitions

Campostrini, Massimo; Nespolo, Jacopo; Pelissetto, Andrea; Vicari, Ettore

doi:10.1103/physrevlett.113.070402

Cited by 61 publications

(197 citation statements)

References 32 publications

(66 reference statements)

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“…2 as a function of density, display a clear transition between the solid and liquid states. As our simulated system is finite, the sharpness of this transition is in fact a remarkable occurrence [46][47][48]. Despite effort, we were not able to detect any smooth rollover between the phases.…”

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confidence: 74%

Quantum phase transition with a simple variational ansatz

et al. 2014

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We study the zero-temperature quantum phase transition between liquid and hcp solid 4 He. We use the variational method with a simple yet exchange-symmetric and fully explicit wave function. It is found that the optimized wave function undergoes spontaneous symmetry breaking and describes the quantum solidification of helium at 22 atm. The explicit form of the wave function allows us to consider various contributions to the phase transition. We find that the employed wave function is an excellent candidate for describing both a first-order quantum phase transition and the ground state of a Bose solid. Properties of solid 4 He have regained attention due to a host of unexpected physics discovered in the past decade [1][2][3][4][5][6][7][8]. Most of the new features occur close to absolute zero and are believed to be primarily driven by quantum effects. Consequently, the solidification of 4 He came under renewed scrutiny. The role of quantum statistics in the transition location has been recently revisited in Ref. [9]. At small but nonzero temperatures, indistinguishability of particles destabilizes the quantum solid. Distinguishable particles, on the other hand, would solidify even at low pressures, with the phase diagram reminiscent of the Pomeranchuk effect [10,11]. The feature was dubbed in [9] as thermocrystallization. A similar effect was seen numerically for the Wigner-crystallization of a two-dimensional Coulomb system [12]. The solidification of 4 He at zero temperature was revisited in Ref. [13] with the density functional theory (DFT). Results were improved compared with previous DFT studies.In this paper, we show that the quantum solidification of 4 He can be considered variationally, with a single explicit wave-function which selects the phase through optimization of the thermodynamic potential. Quite surprisingly, we find that the phase transition is predicted properly, given the relative simplicity of the wave function. While the variational treatment is used for quantum phase transitions at the mean-field level [14], it is relatively uncommon that a (discontinuous) transition can be described with a microscopic wave function. The finding is also interesting in light of growing interest to the first-order quantum phase transitions [15,16].At zero temperature, the phases of 4 He can be studied in an essentially exact form with a family of projector methods, including Green's-function Monte Carlo [17,18] [23,24], and describe the transition [25][26][27] and coexistence [28] between the two phases. The SWFs can be seen as representing a single step of a projection calculation [23]. The projection is carried out by performing the numerical integration of the shadow degrees of freedom. In this sense, the SWF is not fully explicit, as one cannot write down the result of such an integration. We consider SWF calculations as a class of their own, in between the exact projection methods and the simple and fully explicit wave function used here.Highly effective wave functions have been developed over the years...

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confidence: 74%

Quantum phase transition with a simple variational ansatz

et al. 2014

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“…Some details of the DMRG implementation can be found in Refs. [64,65], where we presented numerical studies of the same models in homogeneous conditions. From the numerical point of view, simulations of the inhomogeneous system do not present any additional difficulty.…”

Section: Quantum Ising and Potts Chainsmentioning

confidence: 99%

“…Therefore, in the p -> oo limit the scaling behavior predicted by the general theory for generic values of p must reproduce the finite-size behavior of the corresponding homogeneous system. Although at FOQTs there is no diverging correlation length in the infinite-volume limit, one can observe FSS close to the transition point, both in the case of classical and quantum first-order transitions [64,65,75,[79][80][81][82][83][84][85][86][87][88][89][90]. The relevant FSS variable at a FOQT is the ratio k = EL/A L between the energy contribution EL of the perturbation driving the transition and the energy difference (gap) of the lowest states Al = E\ -Eq at the transition point.…”

Section: Scaling Behavior In the Crossover Space Regionmentioning

confidence: 99%

“…We wish now to extend these FSS scaling relations [64] to the inhomogeneous case. In the presence of inhomogeneous fields whose space behavior is given by Eq.…”

Section: Scaling Behavior In the Crossover Space Regionmentioning

confidence: 99%

“…In homogeneous systems [64,91] the states J2xe'px\x) with momenta p of order L " 1 are eigenstates of the Hamiltonian with FOBC, with energies that differ by terms of order 1 /L2 from that of the ground state. We expect these states to provide the lowest eigenstates even in the presence of a linearly varying magnetic field hx = x/£.…”

Section: Scaling Phenomena Induced By the Inhomogeneous Fieldsmentioning

confidence: 99%

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Scaling phenomena driven by inhomogeneous conditions at first-order quantum transitions

et al. 2015

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We investigate the effects of smooth inhomogeneities at first-order quantum transitions (FOQTs), such as those arising in the presence of a space-dependent external field, which smooths out the discontinuities of the low-energy properties at the transition. We argue that a universal scaling behavior emerges in the space transition region close to the point in which the external field takes the value for which the homogeneous system undergoes the FOQT. We verify the general theory in two model systems. We consider the quantum Ising chain in the ferromagnetic phase and the q-state Potts chain for q=10, investigating the scaling behavior which arises in the presence of an additional inhomogeneous parallel and transverse magnetic field, respectively. Numerical results are in full agreement with the general theory.

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Common Scaling Functions in Dynamical and Quantum Phase Transitions

Nemoto

2015

Phenomenological Structure for the Large Deviation Principle in Time-Series Statistics

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Finite-Size Scaling at First-Order Quantum Transitions

Cited by 61 publications

References 32 publications

Quantum phase transition with a simple variational ansatz

Quantum phase transition with a simple variational ansatz

Scaling phenomena driven by inhomogeneous conditions at first-order quantum transitions

Common Scaling Functions in Dynamical and Quantum Phase Transitions

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