Deconfined criticality, runaway flow in the two-component scalar electrodynamics and weak first-order superfluid-solid transitions

Kuklov, Anatoly; Prokof’ev, Nikolay; Svistunov, Boris; Troyer, Matthias

doi:10.1016/j.aop.2006.04.007

Cited by 117 publications

(166 citation statements)

References 25 publications

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“…However, more detailed studies failed to confirm their existence. Instead, many studies have pointed to a weakly first-order antiferromagnetic-VBS transition [35,36,37,38,39] or other scenarios inconsistent with deconfined criticality [40]. However, recent quantum monte carlo studies on a particular model by Sandvik [41] shows a Néel-VBS phase transition consistent with the deconfined quantum critical point scenario.…”

Section: Discussionmentioning

confidence: 99%

Deconfined Quantum Critical Points

Senthil

Vishwanath

Sachdev

et al. 2010

The Multifaceted Skyrmion

114

223

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The theory of second order phase transitions is one of the foundations of modern statistical mechanics and condensed matter theory. A central concept is the observable 'order parameter', whose non-zero average value characterizes one or more phases and usually breaks a symmetry of the Hamiltonian. At large distances and long times, fluctuations of the order parameter(s) are described by a continuum field theory, and these dominate the physics near such phase transitions. In this paper we show that near second order quantum phase transitions, subtle quantum interference effects can invalidate this paradigm. We present a theory of quantum critical points in a variety of experimentally relevant two-dimensional antiferromagnets. The critical points separate phases characterized by conventional 'confining' order parameters. Nevertheless, the critical theory contains a new emergent gauge field, and 'de-1 confined' degrees of freedom associated with fractionalization of the order parameters. We suggest that this new paradigm for quantum criticality may be the key to resolving a number of experimental puzzles in correlated electron systems.

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Section: Discussionmentioning

confidence: 99%

Deconfined Quantum Critical Points

Senthil

Vishwanath

Sachdev

et al. 2010

The Multifaceted Skyrmion

114

223

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“…6] in the JQ model. Analogous computations in the CP 1 model, although currently unavailable [15] are highly desirable to further demonstrate that the JQ model realizes this new and exotic class of quantum criticality.…”

Section: Basis and Sign Of Matrix Elementsmentioning

confidence: 99%

Scaling in the Fan of an Unconventional Quantum Critical Point

2008

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We present results of extensive finite-temperature Quantum Monte Carlo simulations on a SU(2) symmetric S = 1/2 quantum antiferromagnet with a four-spin interaction [Sandvik, Phys. Rev. Lett. 98, 227202 (2007)]. Our simulations, which are free of the sign-problem and carried out on lattices containing in excess of 1.6 × 10 4 spins, indicate that the four-spin interaction destroys the Néel order at an unconventional z = 1 quantum critical point, producing a valence-bond solid paramagnet. Our results are consistent with the 'deconfined quantum criticality' scenario.Research into the possible ground states of SU(2) symmetric quantum antiferromagnets has thrived over the last two decades, motivated to a large extent by the undoped parent compounds of the cuprate superconductors. In these materials, the Cu sites can be well described as S = 1/2 spins on a two-dimensional (2D) square lattice that interact with an anti-ferromagnetic exchange, the archetypal model for which is the Heisenberg model. By now, it is well established [1] that the ground state of this model with nearest-neighbor interaction has Néel order that spontaneously breaks the SU(2) symmetry. Two logical questions immediately arise: What possible paramagnetic ground states can be reached by tuning competing interactions that destroy the Néel state? Are there universal quantum-critical points (QCP) that separate these paramagnets from the Néel phase?An answer to the first question is to disorder the Néel state by the proliferation of topological defects in the Néel order parameter [2]. It was shown by Read and Sachdev [3] that the condensation of these defects in the presence of quantum Berry phases results in a fourfold degenerate paramagnetic ground state, which breaks square-lattice symmetry due to the formation of a crystal of valence bonds -a valence-bond solid (VBS) phase. An answer to the second question was posed in recent work by Senthil et al.[4], where the possibility of a direct continuous Néel-to-VBS transition was proposed. The natural field theoretic description of this 'deconfined quantum critical point' is written in terms of certain fractionalized fields that are confined on either side of the QCP and become 'deconfined' precisely at the critical point. As is familiar from the general study of QCPs, these fractional excitations are expected to influence the physics in a large fan-shaped region that extends above the critical point at finite-T [5] (see Fig. 1).It is clearly of great interest to find models that harbor a direct Néel-VBS QCP and that can be studied without approximation on large lattices. Currently, the best candidate is the 'JQ' model, introduced by Sandvik [6], which is an S = 1/2, SU(2) invariant antiferromagnet (ii) In the 'quantum critical fan', there is scaling behavior characteristic of a z = 1 QCP; (iii) An accurate estimate of the scaling dimension of the Néel field establishes that this transition is not in the O(3) universality class; and, (iv) The paramagnetic ground state for sufficiently small J/Q is a V...

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“…which has been popular in the study of the DCPs [6], we turn to W 2 (which is related to the spin stiffness as βρ s ). At a first order transition one expects a linear divergence of W 2 as one approaches the phase transition since ρ s stays finite.…”

Section: Metry Of the S-cpmentioning

confidence: 99%

“…A self-duality in the field theory suggested that this could be the best candidate for a deconfined critical point [5]. Subsequent numerical work has concluded however that this transition is first order, both in direct discretizations of the field theory [6,7] as well as in simulations of the quantum anti-ferromagnet [8]. The easy-plane case is in contrast to the symmetric SU(N ) case (we refer to this as s-SU(N )), where striking agreement between technical field theoretic calculations [9][10][11][12] and numerical simulations of the quantum magnets has been demonstrated [13][14][15].…”

mentioning

confidence: 99%

New Easy-Plane CPN−1 Fixed Points

D’Emidio

Kaul

2017

Phys. Rev. Lett.

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We study fixed points of the easy-plane CP N −1 field theory by combining quantum Monte Carlo simulations of lattice models of easy-plane SU(N ) superfluids with field theoretic renormalization group calculations, by using ideas of deconfined criticality. From our simulations, we present evidence that at small N our lattice model has a first order phase transition which progressively weakens as N increases, eventually becoming continuous for large values of N . Renormalization group calculations in 4 − dimensions provide an explanation of these results as arising due to the existence of an Nep that separates the fate of the flows with easy-plane anisotropy. When N < Nep the renormalization group flows to a discontinuity fixed point and hence a first order transition arises. On the other hand, for N > Nep the flows are to a new easy-plane CP N −1 fixed point that describes the quantum criticality in the lattice model at large N . Our lattice model at its critical point, thus gives efficient numerical access to a new strongly coupled gauge-matter field theory.Introduction: The study of anti-ferromagnets has uncovered fascinating connections between quantum spin models and gauge theories. The connections have allowed novel gauge theoretic concepts such as deconfinement to be brought into the realm of condensed matter physics. Turning this mapping around, can the study of magnetism provide non-perturbative insights into gauge theories? Remarkably, advances in simulation algorithms for quantum anti-ferromagnets [1] have recently allowed controlled numerical access to otherwise poorly understood strongly coupled gauge theories; the most prominent example being the CP N −1 gauge theory proposed for deconfined critical points (DCP) in SU(N ) magnets [2].In early work on DCP, a prominent role was played by the "easy-plane SU(2)" [3] magnet and its corresponding "easy-plane CP 1 " field theory [2,4]. A self-duality in the field theory suggested that this could be the best candidate for a deconfined critical point [5]. Subsequent numerical work has concluded however that this transition is first order, both in direct discretizations of the field theory [6,7] as well as in simulations of the quantum anti-ferromagnet [8]. The easy-plane case is in contrast to the symmetric SU(N ) case (we refer to this as s-SU(N )), where striking agreement between technical field theoretic calculations [9][10][11][12] and numerical simulations of the quantum magnets has been demonstrated [13][14][15].The sharp contrast between the easy-plane and symmetric cases has been unexplained so far. In this work we address the first order transition in the easy-plane case using both lattice simulations of an ep-SU(N ) model as well as renormalization group calculations on a proposed ep-CP N −1 field theory. We find the first order transition in the ep-SU(N ) models found for N = 2 in previous work persists for larger N . A careful analysis however shows that the first order jump quantitatively weakens as N increases. Renormalization group -expansion ...

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Deconfined criticality, runaway flow in the two-component scalar electrodynamics and weak first-order superfluid-solid transitions

Cited by 117 publications

References 25 publications

Deconfined Quantum Critical Points

Deconfined Quantum Critical Points

Scaling in the Fan of an Unconventional Quantum Critical Point

New Easy-Plane CPN−1 Fixed Points

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