Renormalization, vortices, and symmetry-breaking perturbations in the two-dimensional planar model

José, Jörge V.; Kadanoff, Leo P.; Kirkpatrick, Scott; Nelson, David R.

doi:10.1103/physrevb.16.1217

Cited by 1,918 publications

(1,400 citation statements)

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“…The sum over in (43) extends over all plaquettes of the cubic lattice, ∆ µ is the standard discrete lattice derivative (∆ µ f j ≡ f j+µ − f j for any f j ), and e 2 is a coupling constant. We expect the value of e to increase monotonically with g. As is standard in duality mappings, we first rewrite the partition function in 2 + 1 spacetime dimensions by replacing the cosine interaction in (43) by a Villain sum [56,57] over periodic Gaussians:…”

Section: Paramagnetic Phasementioning

confidence: 99%

Quantum phases and phase transitions of Mott insulators

Sachdev

2004

Quantum Magnetism

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Summary. This article contains a theoretical overview of the physical properties of antiferromagnetic Mott insulators in spatial dimensions greater than one. Many such materials have been experimentally studied in the past decade and a half, and we make contact with these studies. The simplest class of Mott insulators have an even number of S = 1/2 spins per unit cell, and these can be described with quantitative accuracy by the bond operator method: we discuss their spin gap and magnetically ordered states, and the transitions between them driven by pressure or an applied magnetic field. The case of an odd number of S = 1/2 spins per unit cell is more subtle: here the spin gap state can spontaneously develop bond order (so the ground state again has an even number of S = 1/2 spins per unit cell), and/or acquire topological order and fractionalized excitations. We describe the conditions under which such spin gap states can form, and survey recent theories (T. Senthil et al., cond-mat/0312617) of the quantum phase transitions among these states and magnetically ordered states. We describe the breakdown of the Landau-GinzburgWilson paradigm at these quantum critical points, accompanied by the appearance of emergent gauge excitations.

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Section: Paramagnetic Phasementioning

confidence: 99%

Quantum phases and phase transitions of Mott insulators

Sachdev

2004

Quantum Magnetism

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“…For this, we consider a discrete six-state clock model 26 on a three-dimensional hexagonal lattice as in Ref. 27.…”

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confidence: 99%

Ferroelectricity in the multiferroic hexagonal manganites

et al. 2015

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1The emergence of the spontaneous polarization in the hexagonal RMnO 3 system (R = Sc, Y, In, Dy -Lu) is one of the singular properties and, at the same time, one of the greatest mysteries of this class of compounds. Taking YMnO 3 as reference compound for the series (see Methods), Curie temperatures inexplicably spreading from 910 K to 1250 K have been reported 10-16, 18, 19 . In some of these cases ferroelectricity has been claimed to emerge together with a trimerizing lattice distortion in a single-step transition 16,18,19 . In other cases these two features have been proposed to occur separately [10][11][12][13][14][15] . On the theoretical side, the two-transition scenario has initially been supported by density-functional-theory calculations 20 . A more detailed analysis, however, suggests improper ferroelectricity triggered by the lattice trimerization in a single-step transition 21,22 , in which secondary anomalies are yet possible due to the breaking of residual symmetries 23 . Direct measurement of the spontaneous polarization as function of temperature would clarify this puzzling situation. This was done once in a pyrocurrent measurement which pointed to an onset of ferroelectricity at 933 K 16 . All attempts to reproduce this experiment failed, however. Thus, in spite of 50 years of research, the emergence of the polar order in the hexagonal RMnO 3 multiferroics is surrounded by contradictions. This uncertainty extends to the universality class of this ferroelectric transition, as this basic question depends on the precise nature of the state undergoing the polar instability. The universality class and the corresponding critical behavior determines important physical properties from the macro-to the nanoscale. Understanding such functionalities is infinitely more difficult if the emergence of the ferroelectric order itself is unclear. Thus, for putting the intense research on the unusual properties of ferroelectric order in the hexagonal RMnO 3 system 2, 3, 5,8,9 onto a solid basis, this situation must be resolved. 2Here we present nonlinear optical experiments in which the electromagnetic field of a frequency-doubled light wave couples directly and linearly to the spontaneous polarization of YMnO 3 .They reveal a polarization emerging at T C 1259 K with a subdued increase in amplitude showing no anomalies or discontinuities. Piezoresponse force microscopy (PFM) confirms that the ferroelectric domain pattern is seeded right below T C . Monte-Carlo simulations reveal how topologically created vortex-like defects in the MnO 5 tilt pattern determine the ferroelectric state and many of its unusual properties. In particular, we show that the "second transition" below T C is not associated to a phase transition, but caused by a finite-size scaling effect.At room temperature, the spontaneous polarization P s = 5.6 µC/cm 2 of YMnO 3 is observed together with unit-cell-trimerizing tilts of the MnO 5 bipyramids and Y displacements along the c axis. The tilt is parameterized 22, 23 by the observable amplitude ...

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“…In 1+1 dimensions, it * Electronic address: fcooper@lanl.gov † Electronic address: john.dawson@unh.edu ‡ Electronic address: bogdan.mihaila@unh.edu is known that there is no phase transition in this model except at zero temperature [3]. On the other hand, in two dimensional systems having Berezinski-KosterlitzThouless type transitions [4,5,6], the large-N expansion can give qualitatively good understanding of the correlation functions, even when it gives the wrong phase transition behavior [7]. As the dimensions increase, the mean field critical behavior becomes exact in four dimensions and thus we expect that the approximation presented here should improve as we increase the dimensionality.…”

Section: Introductionmentioning

confidence: 99%

Quantum dynamics of phase transitions in broken symmetryλφ4field theory

2003

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We perform a detailed numerical investigation of the dynamics of a single component broken symmetry λ φ 4 field theory in 1+1 dimensions using a Schwinger-Dyson equation truncation scheme based on ignoring vertex corrections. In an earlier paper, we called this the bare vertex approximation (BVA). We assume the initial state is described by a Gaussian density matrix peaked around some non-zero value of φ(0) , and characterized by a single particle Bose-Einstein distribution function at a given temperature. We compute the evolution of the system using three different approximations: Hartree, BVA and a related 2PI-1/N expansion, as a function of coupling strength and initial temperature. In the Hartree approximation, the static phase diagram shows that there is a first order phase transition for this system. As we change the initial starting temperature of the system, we find that the BVA relaxes to a new final temperature and exhibits a second order phase transition. We find that the average fields thermalize for arbitrary initial conditions in the BVA, unlike the behavior exhibited by the Hartree approximation, and we illustrate how φ(t) and χ(t) depend on the initial temperature and on the coupling constant. We find that the 2PI-1/N expansion gives dramatically different results for φ(t) .

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Renormalization, vortices, and symmetry-breaking perturbations in the two-dimensional planar model

Cited by 1,918 publications

References 30 publications

Quantum phases and phase transitions of Mott insulators

Quantum phases and phase transitions of Mott insulators

Ferroelectricity in the multiferroic hexagonal manganites

Quantum dynamics of phase transitions in broken symmetryλφ4field theory

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