Quantum melting in a system of rotors

Freǐman, Yu. A.; Sumarokov, V. V.; Brodyanskii, A. P.; Jeżowski, A.

doi:10.1088/0953-8984/3/21/018

Cited by 17 publications

(22 citation statements)

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“…[22]. A similar behavior was already discovered in mean-field studies of certain quantum Ising models [24], quantum four-state clock models with quadrupolar interactions [28] and interacting 3D quadrupolar rotators [31]. The reentrance in the two-level systems was also found to be present when fluctuations were included to lowest order in form of a Kirkwood correction on top of the Bragg-Williams expressions [24].…”

Section: Motivationsupporting

confidence: 77%

Quantum fluctuations driven orientational disordering: A finite-size scaling study

1997

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The orientational ordering transition is investigated in the quantum generalization of the anisotropic-planar-rotor model in the low temperature regime.The phase diagram of the model is first analyzed within the mean-field approximation. This predicts at T = 0 a phase transition from the ordered to the disordered state when the strength of quantum fluctuations, characterized by the rotational constant Θ, exceeds a critical value Θ M F c . As a function of temperature, mean-field theory predicts a range of values of Θ where the system develops long-range order upon cooling, but enters again into a disordered state at sufficiently low temperatures (reentrance). The model is further studied by means of path integral Monte Carlo simulations in combination with finite-size scaling techniques, concentrating on the region of parameter space where reentrance is predicted to occur. The phase diagram determined from the simulations does not seem to exhibit reentrant behavior; at intermediate temperatures a pronounced increase of short-range order is observed rather 1 than a genuine long-range order. 05.70.Fh, 64.60.Cn, 68.35.Rh Typeset using REVT E X 2 I. MOTIVATIONPhysisorbates are experimental realizations of quasi two-dimensional systems that display an extremely rich phase behavior due to the competition between intermolecular and molecule-surface interactions, as documented, e.g., in Refs. [1][2][3][4][5]. Correspondingly there is a wealth of phase transitions between the various ordered phases as a function of temperature and coverage. Since many of these transitions occur at fairly low temperatures, quantum effects might play an important or even crucial role [3,4], as recently demonstrated for the ordering of hydrogen isotopes on graphite [6]. Molecular systems are particularly interesting as they possess orientational degrees of freedom which can order in addition to the positions [5].In case of linear molecules, the anisotropic-planar-rotor (APR) model [7,8] was devised to describe the herringbone (quadrupolar orientational two-sublattice) ordering transition [5], e.g., in commensurate N 2 monolayers on graphite. The classical two-dimensional APR model consists of planar rotators pinned with their center of rotation on a triangular lattice and interacting via nearest-neighbor quadrupolar interactions only; a three-dimensional version has also been proposed and investigated in various approximations [9].Over the years the APR Hamiltonian acquired the status of a statistical mechanical model on its own right, see Refs. [10,5]. Many of these activities arose because the order of the APR phase transition turned out to be extremely challenging to determine [11], finally favoring a first order phase transition that is "weak" and fluctuation driven [12], see the detailed review in Ref. [5]. The plain APR model was generalized to include vacancies or impurities [13][14][15], as well as multipole interactions other than those of quadrupolar symmetry [14,16]. Simplified Hamiltonians were obtained after discreti...

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Section: Motivationsupporting

confidence: 77%

Quantum fluctuations driven orientational disordering: A finite-size scaling study

1997

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“…The main difference between the phase diagrams of odd-J and even-J systems is accurately captured, namely that at low pressures odd-J systems are always ordered, whereas even-J systems order at finite pressures. As expected from experiment odd-J D 2 orders at a lower coupling strength than odd-J H 2 , and the reentrant phase transition in HD is also well reproduced by mean-field theory [6,7,8].…”

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confidence: 82%

“…The zero-temperature orientationally disordered phase is characterized by an energy gap against J = 1 excitations. When this gap is sufficiently small and the temperature is finite, the thermally generated J = 1 excitations suffice to induce ordering, which is then reentrant, as also shown by mean-field the- ory [6,7,8]. Reentrance is also found in models of twodimensional rotors [9], such as the quantum anisotropic planar rotor (QAPR) model [10,11,12].…”

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confidence: 93%

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Theoretical Evidence for a Reentrant Phase Diagram in Ortho-Para Mixtures of SolidH2at High Pressure

2005

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We develop a multi order parameter mean-field formalism for systems of coupled quantum rotors. The scheme is developed to account for systems where ortho-para distinction is valid. We apply our formalism to solid H2 and D2. We find an anomalous reentrant orientational phase transition for both systems at thermal equilibrium. The correlation functions of the order parameter indicate short-range order at low temperatures. As temperature is increased the correlation increases along the phase boundary. We also find that even extremely small odd-J concentrations (1%) can trigger short-range orientational ordering.PACS numbers: 61.43.-j,64.70.-p,67.65.+z Quantum effects dominate the low temperature (T < 200K) phase diagram of solid molecular hydrogen in a wide range of pressures from ambient up to ∼ 100 GPa [1,2]. In this regime the coupling between molecules is smaller than the molecular rotational constant, so quantum effects are generally described by means of weakly coupled quantum-rotor models [3]. Homonuclear molecules (H 2 and D 2 ) can assume only even or odd values of the rotational quantum number J, depending on the parity of the nuclear spin. Important differences exist in the phase diagrams of even-J (para-H 2 and ortho-D 2 ), odd-J (ortho-H 2 and para-D 2 ) and all-J (HD) species. (For a summary of experimental results on the orientational ordering in H 2 , D 2 , and HD see Fig. 1b of reference 4.) At low pressure or high temperature, even-J species are found in a rotationally disordered free-rotor state (phase I). Increasing pressure causes an increase of the intermolecular coupling, and eventually leads to an orientationally ordered state (phase II). Odd-J systems on the other hand are orientationally ordered at low temperature and ambient pressure and remain ordered as pressure is increased. The stronger tendency of ortho-H 2 to order can be traced to the fact that its J = 1 lowest rotational state allows for a spherically asymmetric ground state, unlike the J = 0 ground state of even-J species. The pressure-temperature phase diagram of HD exhibits a peculiar reentrant shape [5]. Reentrance refers to phase diagrams where in some range of pressure the system reenters the disordered phase at ultra-low temperatures (see HD in Fig. 1). The zero-temperature orientationally disordered phase is characterized by an energy gap against J = 1 excitations. When this gap is sufficiently small and the temperature is finite, the thermally generated J = 1 excitations suffice to induce ordering, which is then reentrant, as also shown by mean-field the- * Present address

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“…8 are readily obtained by adopting for such a trial wave function a linear combination of spherical harmonics. This approach has been successfully used for other quantum rotor systems, for example, diatomic solids and solid methane, and it has also been applied to the ground state of solid hydrogen (26)(27)(28)(29)(30)(31)(32) at lower pressures. We therefore proceed with an initial specification of the field parameters E q q , E d d , E d q , and E q d , all of which eventually depend on the structure, and of the density r s (which for a given temperature may be converted via the equation of state to a pressure p).…”

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confidence: 99%

Order in dense hydrogen at low temperatures

Edwards

Ashcroft²

2004

Proc. Natl. Acad. Sci. U.S.A.

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By increase in density, impelled by pressure, the electronic energy bands in dense hydrogen attain significant widths. Nevertheless, arguments can be advanced suggesting that a physically consistent description of the general consequences of this electronic structure can still be constructed from interacting but state-dependent multipoles. These reflect, in fact self-consistently, a disorder-induced localization of electron states partially manifesting the effects of proton dynamics; they retain very considerable spatial inhomogeneity (as they certainly do in the molecular limit). This description, which is valid provided that an overall energy gap has not closed, leads at a mean-field level to the expected quadrupolar coupling, but also for certain structures to the eventual emergence of dipolar terms and their coupling when a state of broken charge symmetry is developed. A simple Hamiltonian incorporating these basic features then leads to a high-density, low-temperature phase diagram that appears to be in substantial agreement with experiment. In particular, it accounts for the fact that whereas the phase I-II phase boundary has a significant isotope dependence, the phase II-III boundary has very little.A t low temperatures and ordinary pressure, crystalline hydrogen has a mean electronic density that exceeds the valence electron density of all the alkali metals and even the alkaline earths under equivalent conditions. However, it is a ground state insulator retaining this physical characteristic at densities an entire order of magnitude higher than its one atmosphere value. Under these compressions application of band theory for rigorously static lattices shows clearly that the electronic energy bands of hydrogen are appreciably wide, indicating significant overlap between the standard orbitals invoked to describe the low density phases. Yet much of the electronic charge remains well localized in the vicinity of a Bohr radius from the protons, and there is evidence that the currently accessible part of the low temperature, high density phase diagram can still be understood in terms of interactions originating with multipole expansions associated with effectively localized states and a continuing preservation of the strongly inhomogeneous character of the microscopic electron density e (1) (r). The deeper understanding of this notion, and its consequences, constitutes the bulk of what follows, but starting from an elementary observation that a macroscopic neutral quantity of hydrogen is but a dual Fermion assembly of electrons and protons, and that the dynamics of the latter have considerable influence on the former. The Dense Hydrogen ProblemThe quantum mechanics of N(ϳ10 23 ) electrons in a uniform compensating charged continuum of volume V is a well studied problem, though debate still continues on the nature of its low density states (especially in reduced dimensionality). If v c (r) ϭ e 2 ͞r is the fundamental Coulomb interaction, and if e ϭ e(N͞V) is the corresponding rigid continuum charge density, the...

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Quantum melting in a system of rotors

Abstract: We consider a simple system of interacting rotators and show that such a system could display properties of quantum crystals. The possibility of realizing new quantum system is discussed

Cited by 17 publications

References 1 publication

Quantum fluctuations driven orientational disordering: A finite-size scaling study

Quantum fluctuations driven orientational disordering: A finite-size scaling study

Theoretical Evidence for a Reentrant Phase Diagram in Ortho-Para Mixtures of SolidH2at High Pressure

Order in dense hydrogen at low temperatures

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