Quantum critical scaling at a Bose-glass/superfluid transition: Theory and experiment for a model quantum magnet

Yu, Rong; Miclea, C.; Weickert, Franziska; Movshovich, R.; Paduan-Filho, A.; Zapf, V. S.; Roscilde, Tommaso

doi:10.1103/physrevb.86.134421

Cited by 32 publications

(71 citation statements)

References 52 publications

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“…4 where ν = 0.88 (5) is deduced from the log-log plot off derivatives. This result is in full agreement with previous findings [9,14]. We now proceed to the evaluation of the criticaltemperature exponent φ from accurate measurements of T c (∆) (using similar FSS analysis) and the power-law T c = Aδ φ fit to the lowest transition temperatures, see Fig.…”

supporting

confidence: 72%

“…In striking contrast to Fig. 1 and previously reported results [1,9], all data points nicely follow the power-law curve T c ∝ (8.83 − ∆)…”

contrasting

confidence: 52%

“…[8] argues that finite κ at the SF-BG critical point might come from the regular analytic (rather than singular critical) part of the free energy, and, thus, z < d should be considered as an undetermined critical exponent. Moreover, recent experiments on magnetic systems [1], as well as quantum Monte Carlo simulations of related disordered S = 1 antiferromagnets with single-ion anisotropy [9], which use magnetic field (equivalent to the chemical potential in the bosonic system) as a control parameter to drive the system to quantum criticality, report compelling evidence that the values φ ≈ 1.1(1) and ν ≈ 0.75(10) are in strong violation of the key relation φ = zν and the bound φ ≥ 2. As a result, finite-temperature scaling relations used to describe SF-BG criticality for decades, are challenged.…”

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confidence: 99%

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Critical Exponents of the Superfluid–Bose-Glass Transition in Three Dimensions

et al. 2014

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Recent experimental and numerical studies of the critical-temperature exponent φ for the superfluid-Bose glass universality in three-dimensional systems report strong violations of the key quantum critical relation, φ = νz, where z and ν are the dynamic and correlation length exponents, respectively, and question the conventional scaling laws for this quantum critical point. Using Monte Carlo simulations of the disordered Bose-Hubbard model, we demonstrate that previous work on the superfluid-to-normal fluid transition-temperature dependence on chemical potential (or magnetic field, in spin systems), Tc ∝ (µ − µc) φ , was misinterpreting transient behavior on approach to the fluctuation region with the genuine critical law. When the model parameters are modified to have a broad quantum critical region, simulations of both quantum and classical models reveal that the φ = νz law [with φ = 2.7(2), z = 3, and ν = 0.88(5)] holds true, resolving the φ-exponent "crisis".PACS numbers: 67.85. Hj,64.70.Tg Disordered Bose-Hubbard (DBH) model is frequently employed as a key prototype system to discuss and understand a number of important experimental cases, such as 4 He in porous media and on various substrates, thin superconducting films, cold atoms in disordered optical lattice potentials, and disordered magnets (see [1,2] and references therein), etc.The pioneering work [3,4] on the DBH model has established that at T = 0 an insulating Bose glass (BG) phase will emerge as a result of localization effects in disordered potentials. On a lattice, this phase will intervene between the Mott-insulator (MI) and superfluid (SF) phases at arbitrary weak disorder strength [4,5] and completely destroy the MI phase at strong disorder. In contrast with the gapped incompressible MI phase, the BG phase has finite compressibility, κ, due to finite density of localized gapless quasiparticle and quasihole excitations. Using scaling arguments, and the fact that κ = const at the critical point of the quantum SF-BG transition, it was predicted that the dynamic critical exponent, z, always equals the dimension of space; i.e., z = d [4]. The decrease of the normal-to-superfluid transition temperature, T c , on approach to the quantum critical point (QCP) is characterized by the φ exponent:where g is the control parameter used to reach the QCP. Standard scaling analysis of the quantum-critical free-energy density predicts that φ has to satisfy the relation φ = νz. Therefore, taking into account Harris criterion ν ≥ 2/d [6] for the correlation length exponent in disordered systems, it is expected that φ ≥ 2, within the standard picture of quantum critical phenomena.Despite substantial research efforts in the last two decades, some aspects of the universal critical behavior described above remain controversial (see, e.g., Ref. [7]).For instance, Ref. [8] argues that finite κ at the SF-BG critical point might come from the regular analytic (rather than singular critical) part of the free energy, and, thus, z < d should be considered as an undet...

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supporting

confidence: 72%

“…In striking contrast to Fig. 1 and previously reported results [1,9], all data points nicely follow the power-law curve T c ∝ (8.83 − ∆)…”

contrasting

confidence: 52%

mentioning

confidence: 99%

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Critical Exponents of the Superfluid–Bose-Glass Transition in Three Dimensions

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“…Energy of the impurity states bring new physics above H c2 where a Bose-glass (BG) regime [3,4] with a disordered many-body groundstate was recently reported [37,38]. However, the Br-doped bonds introduce a new energy scale in DTNX, as shown by an enhanced NMR relaxation around a cross-over field H * 13.6 T [28].…”

mentioning

confidence: 99%

“…Upon increasing further the field H > H * , we then expect the BEC * dome to eventually vanish, presumably before H c2 16.7 T for x < 15.6% (where the Br-doped cluster reaches its percolation threshold), thus offering the possibility to stabilize another Bose-glass state at high magnetic field, before the complete saturation of the spins. It is therefore quite promising to contemplate this BEC -Bose glass criticality at such a high-field transition where no surrounding order would spoil its genuine properties, allowing to determine its critical exponents which are still controversial [38,65,66]. For other experimental systems with a magnetic Bose glass regime (for a recent review, see Ref.…”

mentioning

confidence: 99%

Disorder-Induced Revival of the Bose-Einstein Condensation inNi(Cl1−xBrx
Dupont
¹
,
Capponi
²
,
Laflorencie
³

2017
Phys. Rev. Lett.
14
5
28
0
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Building on recent NMR experiments [A. Orlova et al., Phys. Rev. Lett. 118, 067203 (2017)], we theoretically investigate the high magnetic field regime of the disordered quasi-one-dimensional S = 1 antiferromagnetic material Ni(Cl1−xBrx)2-4SC(NH2)2. The interplay between disorder, chemically controlled by Br-doping, interactions, and the external magnetic field, leads to a very rich phase diagram. Beyond the well-known antiferromagnetically ordered regime, analog of a Bose condensate of magnons, which disappears when H ≥ 12.3 T, we unveil a resurgence of phase coherence at higher field H ∼ 13.6 T, induced by the doping. Interchain couplings stabilize finite temperature long-range order whose extension in the field -temperature space is governed by the concentration of impurities x. Such a "mini-condensation" contrasts with previously reported Bose-glass physics in the same regime, and should be accessible to experiments.Introduction.-Interacting quantum systems in the presence of disorder have been intensively studied for several decades, leading to fascinating physics, e.g. the Kondo effect [1], the many-body localization transition [2], or the superfluid to Bose-glass (BG) [3,4] transition at finite disorder for lattice bosons [5][6][7]. While counterintuitive, in some situations disorder may enhance long-range order, as discussed for inhomogeneous superconductors [8][9][10]. Perhaps even more surprisingly, doping gapped antiferromagnets with a finite concentration of magnetic or non-magnetic impurities can fill up the bare spin gap with localized levels [11-13] which may eventually order, in the strict sense of macroscopic long-range order (LRO) at low temperature. Such an impurity-induced ordering mechanism of the type "order from disorder" [14,15] [21]. Nevertheless, only a few studies have focused on the effect of an external field [22][23][24][25][26][27].In this Letter, building on recent nuclear magnetic resonance (NMR) experiments [28], we achieve a realistic theoretical study of the high magnetic field regime of Ni(Cl 1−x Br x ) 2 -4SC(NH 2 ) 2 (DTNX): a threedimensional antiferromagnetic (AF) system made of weakly coupled chains of S = 1 spins subject to singleion anisotropy [panels (b-c) of Fig. 1]. Note that the S = 1 chains are not of Haldane type, due to the large anisotropy D [29]. In the absence of chemical disorder (x = 0), NiCl 2 -4SC(NH 2 ) 2 (DTN) provides a very good realization of magnetic field-induced Bose-Einstein condensation (BEC) in a quantum spin system [30][31][32][33] between two critical field H clean

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Quantum Transition Between Magnetically Ordered and Mott Glass Phases

Syromyatnikov

2017

Annalen der Physik

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We discuss a quantum transition from a superfluid to a Mott glass phases in disordered Bosesystems by the example of an isotropic spin-1 2 antiferromagnet with spatial dimension d ≥ 2 and with disorder in tunable exchange couplings. Our analytical consideration is based on general properties of a system in critical regime, on the assumption that the magnetically order part of the system shows fractal properties near the transition, and on a hydrodynamic description of long-wavelength magnons in the magnetically ordered ("superfluide") phase. Our results are fully consistent with a scaling theory based on an ansatz for the free energy proposed by M. P. Fisher et al. (Phys. Rev. B 40, 546 (1989)). We obtain z = d − β/ν for the dynamical critical exponent and φ = zν, where φ, β, and ν are critical exponents of the critical temperature, the order parameter, and the correlation length, respectively. The density of states of localized excitations (fractons) is found to show a superuniversal (i.e., independent of d) behavior.PACS numbers: 64.70. Tg, 72.15.Rn, 74.40.Kb I. INTRODUCTIONThe interplay of quantum fluctuations and quenched disorder leads to a variety of unconventional phenomena and special quantum phases which are of great current interest. 1-5 Examples include metal-insulator and superconductorinsulator transitions, heavy-fermion systems, interacting bosons in disordered potential (the so-called dirty bosons), and doped quantum magnets. In the present paper, we discuss effects of disorder on a quantum phase transition (QPT) between a Néel and a dimerized singlet phases in an isotropic quantum spin-1 2 Heisenberg antiferromagnet (HAF) with spatial dimension d ≥ 2 and with tunable spin couplings. Our conclusions should be relevant to various Bose-systems from the same universality class.The Hamiltonian of the model we discuss has the formwhere i, j denote nearest-neighbor sites of a hypercubic d-dimensional lattice. A three-dimensional version of model (1) without disorder is shown in Fig. 1, where thin and bold lines denote spin couplings with exchange constants J > 0 and gJ > 0, respectively. Decreasing g beyond a critical value g c drives the system through a QPT from the dimerized phase to the Néel one. In pure magnets, such transition is described by O(3) nonlinear quantum field theory and characterized by the dynamical critical exponent z = 1 at d ≥ 1. 3 It has attracted much attention in recent years (see, e.g., Refs. 6-10 and references therein). This interest is stimulated by experimental observation of pressure-induced transitions of this kind in TlCuCl 3 , 11-13 KCuCl 3 , 14,15 CsFeCl 3 , 16 and (C 4 H 12 N 2 )Cu 2 Cl 6 17 . In these compounds, the applied pressure changes exchange coupling constants so that the transition occurs at some pressure value.Another way to bring system (1) from the dimerized to a magnetically ordered phase is to apply a magnetic field h. It is well known that a canted antiferromagnetic order arises in a field range h c1 < h < h c2 and all spins are parallel to the mag...

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Quantum critical scaling at a Bose-glass/superfluid transition: Theory and experiment for a model quantum magnet

Cited by 32 publications

References 52 publications

Critical Exponents of the Superfluid–Bose-Glass Transition in Three Dimensions

Critical Exponents of the Superfluid–Bose-Glass Transition in Three Dimensions

Disorder-Induced Revival of the Bose-Einstein Condensation inNi(Cl1−xBrx
Dupont
¹
,
Capponi
²
,
Laflorencie
³

2017
Phys. Rev. Lett.
14
5
28
0
View full text Add to dashboard Cite

Quantum Transition Between Magnetically Ordered and Mott Glass Phases

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Quantum critical scaling at a Bose-glass/superfluid transition: Theory and experiment for a model quantum magnet

Cited by 32 publications

References 52 publications

Critical Exponents of the Superfluid–Bose-Glass Transition in Three Dimensions

Critical Exponents of the Superfluid–Bose-Glass Transition in Three Dimensions

Disorder-Induced Revival of the Bose-Einstein Condensation inNi(Cl1−xBrxDupont1, Capponi2, Laflorencie3 2017Phys. Rev. Lett.145280View full textAdd to dashboardCite

Quantum Transition Between Magnetically Ordered and Mott Glass Phases

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About

Disorder-Induced Revival of the Bose-Einstein Condensation inNi(Cl1−xBrx
Dupont
¹
,
Capponi
²
,
Laflorencie
³

2017
Phys. Rev. Lett.
14
5
28
0
View full text Add to dashboard Cite