Mott-insulator-superfluid-liquid transition in a one-dimensional bosonic Hubbard model: Quantum Monte Carlo method

Kashurnikov, V. A.; Krasavin, А. V.; Svistunov, Boris

doi:10.1134/1.567139

Cited by 43 publications

(43 citation statements)

References 14 publications

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“…where b † i , b i , and n i = b † i b i are the boson creation, annihilation, and particle number operators on site i respectively. The model has a critical point U c ∼ 3.3 [43][44][45][46][47][48][49][50][51][52], which separates a superfluid phase in U < U c from a Mott insulator phase in U > U c . Our setup for the unitary time evolution background is a quench dynamics from Mott phase into to superfluid phase.…”

Section: Model and Methodsmentioning

confidence: 99%

Measurement-induced phase transition: A case study in the nonintegrable model by density-matrix renormalization group calculations

Tang

Zhu

2020

Phys. Rev. Research

163

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We study the effects of local projective measurements on the quantum quench dynamics. As a concrete example, one-dimensional Bose-Hubbard model is simulated by using matrix product state and time evolving block decimation. We map out a global phase diagram in terms of the measurement rate in spatial space and time domain, which demonstrates a volume-to-area law entanglement phase transition. When the measurement rates reach the critical values, we observe a logarithmic growth of entanglement entropy as the sub-system size or evolved time increases. This is akin to the character in the many-body localization, implying a general picture of the dynamical transitions separating quantum systems with different entanglement features. Moreover, we find that the probability distribution of the single-site entanglement entropy distinguishes the volume and area law phases just as the case of disorder-induced many-body localization. This suggests that the different type entanglement phase transitions may be understood as a nonlocalized-to-localized transition. We also investigate the scaling behavior of entanglement entropy and mutual information between two separated intervals, which is indicative of a single universality class and thus suggests a possible unified description of this transition.

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Section: Model and Methodsmentioning

confidence: 99%

Measurement-induced phase transition: A case study in the nonintegrable model by density-matrix renormalization group calculations

Tang

Zhu

2020

Phys. Rev. Research

163

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“…(311) are not necessarily distinct and may coincide with |n KΓ . Calculating all the matrix elements of the operatorĤ ← one can construct the full Hamiltonian matrix.…”

Section: Remarks On Exact Diagonalizationmentioning

confidence: 99%

Ultracold bosons with short-range interaction in regular optical lattices

2016

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During the last decade, many exciting phenomena have been experimentally observed and theoretically predicted for ultracold atoms in optical lattices. This paper reviews these rapid developments concentrating mainly on the theory. Different types of the bosonic systems in homogeneous lattices of different dimensions as well as in the presence of harmonic traps are considered. An overview of the theoretical methods used for these investigations as well as of the obtained results is given. Available experimental techniques are presented and discussed in connection with theoretical considerations. Eigenstates of the interacting bosons in homogeneous lattices and in the presence of harmonic confinement are analyzed. Their knowledge is essential for understanding of quantum phase transitions at zero and finite temperature.

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“…For small J/U , the nearest-neighbor correlations vanish, since only uncorrelated thermal excitations exist deep in the MI regime. As particle-hole pairs emerge with increasing J/U , we observe an increase of nearest-neighbor correlations until a peak value is reached, well before the critical value (J/U ) 1d c ≈ 0.3 [25,26] for the one-dimensional SF-MI transition. The observed signal is a genuine quantum effect because thermally induced particle-hole pairs extend over arbitrary distances and are therefore uncorrelated.…”

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confidence: 91%

Observation of Correlated Particle-Hole Pairs and String Order in Low-Dimensional Mott Insulators

Endres

Cheneau

Fukuhara

et al. 2011

Science

290

341

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Quantum phases of matter are characterized by the underlying correlations of the many-body system. Although this is typically captured by a local order parameter, it has been shown that a broad class of many-body systems possesses a hidden non-local order. In the case of bosonic Mott insulators, the ground state properties are governed by quantum fluctuations in the form of correlated particle-hole pairs that lead to the emergence of a non-local string order in one dimension. Using high-resolution imaging of low-dimensional quantum gases in an optical lattice, we directly detect these pairs with single-site and single-particle sensitivity and observe string order in the one-dimensional case.The realization of strongly correlated quantum manybody systems using ultracold atoms has enabled the direct observation and control of fundamental quantum effects [1][2][3]. A prominent example is the transition from a superfluid (SF) to a Mott insulator (MI), occurring when interactions between bosonic particles on a lattice dominate over their kinetic energy [4][5][6][7][8]. At zero temperature, and in the limit where the ratio of kinetic energy over interaction energy vanishes, particle fluctuations are completely suppressed and the lattice sites are occupied by an integer number of particles. However, at a finite tunnel coupling, but still in the Mott insulating regime, quantum fluctuations create correlated particlehole pairs on top of this fixed-density background, which can be understood as virtual excitations. These particlehole pairs fundamentally determine the properties of the Mott insulator such as its residual phase coherence [9] and lie at the heart of superexchange-mediated spin interactions that form the basis of quantum magnetism in multi-component quantum gas mixtures [10][11][12].In a one-dimensional system, the appearance of correlated particle-hole pairs at the transition point from a superfluid to a Mott insulator is intimately connected to the emergence of a hidden string-order parameter O P [13,14]:Here δn j =n j −n denotes the deviation in occupation of the jth lattice site from the average background density, and k is an arbitrary position along the chain. In the simplest case of a Mott insulator with unity filling * Electronic address: manuel.endres@mpq.mpg.de (n = 1), relevant to our experiments, each factor in the product of operators in Eq. 1 yields −1 instead of +1, when a single-particle fluctuation from the unit background density is encountered. In the superfluid, particle and hole fluctuations occur independently and are uncorrelated, such that O P = 0. However, in the Mott insulating phase, density fluctuations always occur as correlated particle-hole pairs, resulting in O P = 0. For a homogeneous system, O P is expected to follow a scaling of Berezinskii-Kosterlitz-Thouless (BKT) type [15]. Non-local correlation functions, like the string-order parameter defined above, have been introduced in the context of low-dimensional quantum systems. They classify many-body quantum phases that are n...

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Mott-insulator-superfluid-liquid transition in a one-dimensional bosonic Hubbard model: Quantum Monte Carlo method

Cited by 43 publications

References 14 publications

Measurement-induced phase transition: A case study in the nonintegrable model by density-matrix renormalization group calculations

Measurement-induced phase transition: A case study in the nonintegrable model by density-matrix renormalization group calculations

Ultracold bosons with short-range interaction in regular optical lattices

Observation of Correlated Particle-Hole Pairs and String Order in Low-Dimensional Mott Insulators

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