First-Order Phase Transition in Easy-Plane Quantum Antiferromagnets

Kragset, Steinar; Smørgrav, Eivind; Hove, Joakim; Nogueira, Flavio S.; Sudbø, Asle

doi:10.1103/physrevlett.97.247201

Cited by 56 publications

(74 citation statements)

References 28 publications

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“…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].…”

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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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confidence: 99%

New Easy-Plane CPN−1 Fixed Points

D’Emidio

Kaul

2017

Phys. Rev. Lett.

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“…This causes the N -component model without Josephson interactions to have N − 1 superfluid phase transitions and a single superconducting phase transition 17 . For certain values of the gauge charge these transitions will interfere in a non-trivial way, causing the transitions to merge in a single first-order transition 18,19 . The question of the nature of the phase transitions present in Josephson-coupled multiband superconductors is of considerable interest.…”

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confidence: 99%

Current loops, phase transitions, and the Higgs mechanism in Josephson-coupled multicomponent superconductors

Galteland¹,

Sudbø²

2016

Phys. Rev. B

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The N -component London U(1) superconductor is expressed in terms of integer-valued supercurrents. We show that the inclusion of inter-band Josephson couplings introduces monopoles in the current fields, which convert the phase transitions of the charge-neutral sector to crossovers. The monopoles only couple to the neutral sector, and leave the phase transition of the charged sector intact. The remnant non-critical fluctuations in the neutral sector influence the one remaining phase transition in the charged sector, and may alter this phase transition from a 3DXY inverted phase transition into a first-order phase transition depending on what the values of the gauge-charge and the inter-component Josephson coupling are. This preemptive effect becomes more pronounced with increasing number of components N , since the number of charge-neutral fluctuating modes that can influence the charged sector increases with N . We also calculate the gauge-field correlator, and by extension the Higgs mass, in terms of current-current correlators. We show that the onset of the Higgsmass of the photon (Meissner-effect) is given in terms of a current-loop blowout associated with going into the superconducting state as the temperature of the system is lowered.

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“…This regime corresponds to a large v 0 such that |z 1 | 2 ≈ |z 2 | 2 . However, recent Monte Carlo simulations [6,7] performed in this regime showed that the transition is actually (weakly) first-order.…”

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confidence: 96%

“…From the three models considered, only the one associated with an easy-plane antiferromagnet does not exhibit any second-order phase transition, in agreement with the numerical results of Refs. [6] and [7]. Deconfined spinons were shown to govern a second-order phase transition for both the isotropic SU (N ) antiferromagnet and quantum spin nematic systems.…”

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confidence: 99%

“…The main argument [2] behind the concept of deconfined quantum criticality (DQC) is a topological one: spinon deconfinement occurs due to a destructive interference mechanism between the instantons and the Berry phase [2]. This mechanism was recently observed numerically [6] for the case of an easy-plane antiferromagnet. However, in this case the instanton cancellation mechanism leads actually to a weak first-order phase transition [6].…”

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Quantum critical scaling behavior of deconfined spinons

2007

Self Cite

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We perform a renormalization group analysis of some important effective field theoretic models for deconfined spinons. We show that deconfined spinons are critical for an isotropic SU(N) Heisenberg antiferromagnet, if N is large enough. We argue that nonperturbatively this result should persist down to N = 2 and provide further evidence for the so called deconfined quantum criticality scenario. Deconfined spinons are also shown to be critical for the case describing a transition between quantum spin nematic and dimerized phases. On the other hand, the deconfined quantum criticality scenario is shown to fail for a class of easy-plane models. For the cases where deconfined quantum criticality occurs, we calculate the critical exponent η for the decay of the two-spin correlation function to first-order in ǫ = 4 − d. We also note the scaling relation η = d + 2(1 − ϕ/ν) connecting the exponent η for the decay to the correlation length exponent ν and the crossover exponent ϕ. The most remarkable incarnation of the LandauGinzburg theory of phase transitions is the one embodied by Wilson's renormalization group (RG) [1]. According to this point of view, the Landau-Ginzburg theory is uniquely determined by the effective coupling constants obtained by integrating out high-energy modes. In this way, the large distance scaling behavior of different physical quantities is governed by the fixed points in the space of coupling constants. This is the so called LandauGinzburg-Wilson (LGW) paradigm of phase transitions [2]. The LGW paradigm is known to fail in a number of quantum phase transitions. One prominent example is the transition between the Néel state to a valence bond solid (VBS) state in a two-dimensional Mott insulator [3]. This transition features a quantum critical point (QCP), which is at odds with the LGW scenario that would predict a first-order phase transition. The crucial observation in this context is that both phases break symmetries in distinct spaces: the Néel state breaks the SU(2) symmetry of the Hamiltonian, while the paramagnetic VBS state breaks lattice symmetries. A continuous such order-order phase transition would not be captured by a LGW-like point of view [4].For an SU(2) Heisenberg antiferromagnet the spinons z α are the elementary constituents of the spin orientation field n. We have n a = z † σ a z, a = 1, 2, 3, where z = (z 1 , z 2 ) and σ a are the Pauli matrices. This is the so called CP 1 representation of the SU(2) spins. There is an inherent local gauge invariance in this representation, since n remains invariant when the spinon fields change by a local phase factor, i.e., z α → e iθ(x) z α . Thus, it seems to be natural to effectively describe a Mott insulator through a gauge theory coupled to "spinon matter". The gauge field here is an emergent photon: it is dynamically generated as a consequence of the local gauge invariance of n in terms of the spinon fields. Note that only expectation values of gauge-invariant operators can be nonzero, in agreement with Elitzur's theorem [5]. The VB...

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First-Order Phase Transition in Easy-Plane Quantum Antiferromagnets

Cited by 56 publications

References 28 publications

New Easy-Plane CPN−1 Fixed Points

New Easy-Plane CPN−1 Fixed Points

Current loops, phase transitions, and the Higgs mechanism in Josephson-coupled multicomponent superconductors

Quantum critical scaling behavior of deconfined spinons

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