Recent Developments of World-Line Monte Carlo Methods

Kawashima, Naoki; Harada, Kenji

doi:10.1143/jpsj.73.1379

Cited by 129 publications

(153 citation statements)

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“…As such, exploration of TCPs can be a useful strategy for finding novel universality classes of phase transitions. Despite such ubiquity and importance of TCP, understanding of quantum tricriticality remains limited to a phenomenological level because of lack of experiments with flexible controllability and exact numerical simulations on a microscopic model, in contrast to classical one.In this Letter, we use the unbiased numerical method of quantum Monte-Carlo (QMC) based on the Feynmann path integral [20] to show the existence of quantum TCPs in the ground state phase diagram of the two-component Bose-Hubbard model (BHM) on square lattices. This result suggests that quantum tricriticality can realistically be studied in Bose-Bose mixtures trapped in optical lattices, which are subsistent experimental setups [21][22][23][24][25][26].…”

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confidence: 99%

Quantum Tricriticality at the Superfluid-Insulator Transition of Binary Bose Mixtures

Kato¹,

Yamamoto²,

Danshita³

2014

Phys. Rev. Lett.

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Quantum criticality near a tricritical point (TCP) is studied in the two-component Bose-Hubbard model on square lattices. The existence of quantum TCP on a boundary of superfluid-insulator transition is confirmed by quantum Monte Carlo simulations. Moreover, we analytically derive the quantum tricritical behaviors on the basis of an effective field theory. We find two significant features of the quantum tricriticality, that are its characteristic chemical potential dependence of the superfluid transition temperature and a strong density fluctuation. We suggest that these features are directly observable in existing experimental setups of Bose-Bose mixtures in optical lattices.PACS numbers: 03.75. Mn,64.60.Kw,03.75.Hh Rapid development in experiments with ultracold gases confined in optical lattices has advanced the studies of quantum phase transitions (QPTs), thanks to their precise controllability of various parameters, such as external potentials, interparticle interactions, and lattice geometry, over a wide range. Several QPTs that are of close relevance to other condensed matter systems have been realized in experiments, such as superfluid (SF)-Mott insulator (MI) transitions in a variety of lattice geometry [1-4], SF-Bose glass transitions in a random [5, 6] or quasi-periodic [7, 8] potential, magnetic transitions in a tilted [9] or triangular [10, 11] optical lattice, and topological transitions in a double-well optical lattice [12]. Recent experiments have reported even the observation of quantum critical behaviors accompanying the secondorder QPT between vacuum and SF [13], thus providing new opportunities for studying quantum criticality in optical-lattice systems.Tricriticality, or more generally, multicriticality is a fundamental concept in the study of phase transitions [14]. A tricritical point (TCP) marks a point at which a second-order (continuous) phase transition changes to a first-order (discontinuous) phase transition on a single phase boundary in a two parameter phase diagram. Tricriticality has been discussed in the contexts of several condensed matter systems, e.g., FeCl 2 [15], 3 He-4 He mixture [16], and correlated electron matterials [17,18], as well as in quantum chromodynamics [19]. Due to its unique nature unconventional critical properties are expected to -and indeed found to -emerge in the vicinity of a TCP. As such, exploration of TCPs can be a useful strategy for finding novel universality classes of phase transitions. Despite such ubiquity and importance of TCP, understanding of quantum tricriticality remains limited to a phenomenological level because of lack of experiments with flexible controllability and exact numerical simulations on a microscopic model, in contrast to classical one.In this Letter, we use the unbiased numerical method of quantum Monte-Carlo (QMC) based on the Feynmann path integral [20] to show the existence of quantum TCPs in the ground state phase diagram of the two-component Bose-Hubbard model (BHM) on square lattices. This result suggests that qua...

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confidence: 99%

Quantum Tricriticality at the Superfluid-Insulator Transition of Binary Bose Mixtures

Kato¹,

Yamamoto²,

Danshita³

2014

Phys. Rev. Lett.

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“…We use the continuous-time QMC method [39,40] to compute the thermodynamic phase diagram. There is no sign problem because the frustrated terms are diagonal.…”

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Formation of Magnetic Microphases inCa3Co2O6

Kamiya

Batista

2012

Phys. Rev. Lett.

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We study a frustrated quantum Ising model relevant for Ca 3 Co 2 O 6 that consists of a triangular lattice of weakly-coupled ferromagnetic (FM) chains. According to our quantum Monte Carlo (QMC) simulations, the chains become FM and form a three-sublattice "up-up-down" structure for T ≤ T CI . In contrast, long-period spin-density-wave (SDW) microphases are stabilized along the chains for T CI < T < T c . Our mean field solutions reveal a quasi-continuous temperature dependence of the SDW wavelength, implying the existence of metastable states that explain the very slow dynamics observed in Ca 3 Co 2 O 6 . We also discuss implications of microphases for the related multiferroic compounds Ca 3 CoMnO 6 and Lu 2 MnCoO 6 . [3][4][5], the spin-driven "nematic" transition in pnictides [6][7][8][9], and dimensional reduction in BaCuSi 2 O 6 [10,11]. Ca 3 Co 2 O 6 is another example comprising a triangular lattice of FM Ising chains coupled by weak antiferromagnetic (AFM) exchanges. This compound exhibits field-induced magnetization steps whose heights depend on the field sweep history and rate [12][13][14][15][16]. We will show that this out-of-equilibrium behavior has its roots in exotic equilibrium properties that can be extended to the related multiferroic compound Ca 3 Co 2−x Mn x O 6 [17][18][19][20][21][22].The Co 3+ ions (Co II) on the trigonal prism sites of Ca 3 Co 2 O 6 contain 3d 6 localized electrons that generate an S = 2 spin with large Ising-like anisotropy [23][24][25][26]. These ions form a triangular lattice of FM Ising chains along the caxis (Fig. 1) and the structure comprises three sublattices of layers stacked along the c-axis in an ABCABC . . . configuration. Although the AFM inter-chain couplings J 2 and J 3 [27] [ Fig. 1(a)] are an order of magnitude smaller than the intrachain FM exchange, |J 1 | = 2 × 10 K [23, 27], we will show that they strongly affect the intra-chain spin correlations over a window of temperatures below T c .The initial interest in Ca 3 Co 2 O 6 was triggered by the observation of out-of-equilibrium magnetization steps measured below ∼ 8 K and ∼ 3.6 T that appear at regular field intervals. Previous works invoked a "rigid-chain model": every chain is replaced by a single Ising spin by assuming [28][29][30][31][32]. Each spin of the resulting triangular lattice Ising model (TLIM), represents the magnetization of the whole chain and it is flipped if gµ B H overcomes its molecular field. Within this simplified framework, the regular field intervals result from the equally-spaced discrete molecular field spectrum [28]. However, this 2D scenario was challenged by the recent discovery of long-wavelength intra-chain spindensity-wave (SDW) ordering below T c 25 K [16,33,34]. Motivated by this discovery, Chapon initiated the study of a more realistic 3D lattice model by using a random-phase approximation (RPA) which is only valid close to T = T c [35].By combining QMC simulations and mean field (MF) solu-

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“…This is also the rigorous basis of dropping the usual statistical configuration index on lattice partition functions evaluated via the Monte Carlo method, [19]. To be clear, this is not the usual way that the boundary conditions of the continuous-time QMC method in [15] are presented in review articles [20][21]. However, the usual tacit assumption that is presented: that M commutes with t, is only strictly true in the large volume limit.…”

Section: B Continuous-timementioning

confidence: 99%

The partition function zeroes of quantum critical points

Crompton¹

2009

Nuclear Physics B

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The Lee-Yang theorem for the zeroes of the partition function is not strictly applicable to quantum systems because the zeroes are defined in units of the fugacity e h∆τ , and the Euclidean-time lattice spacing ∆τ can be divergent in the infrared (IR). We recently presented analytic arguments describing how a new space-Euclidean time zeroes expansion can be defined, which reproduces Lee and Yang's scaling but avoids the unresolved branch points associated with the breaking of nonlocal symmetries such as parity. We now present a first numerical analysis for this new zeros approach for a quantum spin chain system. We use our scheme to quantify the renormalization group flow of the physical lattice couplings to the IR fixed point of this system. We argue that the generic Finite-Size Scaling (FSS) function of our scheme is identically the entanglement entropy of the lattice partition function and, therefore, that we are able to directly extract the central charge, c, of the quantum spin chain system using conformal predictions for the scaling of the entanglement entropy.

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Recent Developments of World-Line Monte Carlo Methods

Cited by 129 publications

References 59 publications

Quantum Tricriticality at the Superfluid-Insulator Transition of Binary Bose Mixtures

Quantum Tricriticality at the Superfluid-Insulator Transition of Binary Bose Mixtures

Formation of Magnetic Microphases inCa3Co2O6

The partition function zeroes of quantum critical points

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