Exact Local Correlations and Full Counting Statistics for Arbitrary States of the One-Dimensional Interacting Bose Gas

Bastianello, Alvise; Piroli, Lorenzo; Calabrese, Pasquale

doi:10.1103/physrevlett.120.190601

Cited by 93 publications

(131 citation statements)

References 109 publications

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“…This is especially useful for experimental comparisons. The second method calcLocalCorrelator() computes the local n-body correlator through the approach detailed in [21].…”

Section: Resultsmentioning

confidence: 99%

“…Thus, an infinite set of advection equations emerge, which through the thermodynamic Bethe ansatz, can be formulated as a single Euler-scale equation for a quasiparticle distribution. Since the inception of GHD several applications have been added to the framework, such as calculations of entanglement spreading [16][17][18][19], correlation functions [20][21][22], diffusive corrections [23,24], and many others [25][26][27][28]. Recently it has also been demonstrated to capture the dynamics of a cold Bose gas trapped on an atom-chip [29].…”

Section: Introductionmentioning

confidence: 99%

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Introducing iFluid: a numerical framework for solving hydrodynamical equations in integrable models

Møller

Schmiedmayer

2020

SciPost Phys.

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We present an open-source Matlab framework, titled iFluid, for simulating the dynamics of integrable models using the theory of generalized hydrodynamics (GHD). The framework provides an intuitive interface, enabling users to define and solve problems in a few lines of code. Moreover, iFluid can be extended to encompass any integrable model, and the algorithms for solving the GHD equations can be fully customized. We demonstrate how to use iFluid by solving the dynamics of three distinct systems: (i) The quantum Newton's cradle of the Lieb-Liniger model, (ii) a gradual field release in the XXZ-chain, and (iii) a partitioning protocol in the relativistic sinh-Gordon model. 8 4.2 Charges and currents of XXZ model 13 4.3 Partitioning protocol in relativistic sinh-Gordon 15 5 Conclusion 17 A Thermodynamic Bethe ansatz of implemented models 18 A.1 Lieb-Liniger model 18 A.2 XXZ spin chain model 19 A.3 Relativistic sinh-Gordon model 19 B Numerical implementation of GHD equations 20 1 arXiv:2001.02547v1 [cond-mat.stat-mech] 8 Jan 2020 SciPost Physics Submission B.1 Tensor representation and index conventions 20 B.2 Discretized GHD equations 21 References 22

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“…This is especially useful for experimental comparisons. The second method calcLocalCorrelator() computes the local n-body correlator through the approach detailed in [21].…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Introducing iFluid: a numerical framework for solving hydrodynamical equations in integrable models

Møller

Schmiedmayer

2020

SciPost Phys.

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“…Being a very natural concept FCS has been studied for a long time in different communities. It has been studied in the context of charge fluctuations 45,46 , Bose gases [47][48][49][50][51] , particle number fluctuations [52][53][54][55][56] , quantum spin chains [57][58][59][60][61][62][63][64] and out of equilibrium quantum systems 51,65,66 .…”

Section: Introductionmentioning

confidence: 99%

Formation probabilities and statistics of observables as defect problems in free fermions and quantum spin chains

Najafi

Rajabpour

2020

Phys. Rev. B

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We show that the computation of formation probabilities (FP) in the configuration basis and the full counting statistics (FCS) of observables in the quadratic fermionic Hamiltonians are equivalent to the calculation of emptiness formation probability (EFP) in the Hamiltonian with a defect. In particular, we first show that the FP of finding a particular configuration in the ground state is equivalent to the EFP of the ground state of the quadratic Hamiltonian with a defect. Then, we show that the probability of finding a particular value for any quadratic observable is equivalent to a FP problem and ultimately leads to the calculation of EFP in the ground state of a Hamiltonian with a defect. We provide new exact determinant formulas for the FP in the generic quadratic fermionic Hamiltonians. As applications of our formalism we study the statistics of the number of particles and kinks. Our conclusions can be extended also to the quantum spin chains that can be mapped to the free fermions via Jordan-Wigner (J-W) transformtion. In particular, we provide an exact solution to the problem of the transverse field XY chain with a staggered line defect. We also study the distribution of magnetization and kinks in the transverse field XY chain and show how the dual nature of these quantities manifest itself in the distributions.

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“…Only in recent time, the attention shifted to observables with support on a finite, but large, subsystem embedded in a thermodynamic one, partially motivated by some cold atomic experiments [1][2][3][4][5][6] and by the connection with the entanglement entropy of the same subsystem [7][8][9][10][11][12][13][14][15][16]. In spite of a large recent literature on the subject , results based on integrability for one-dimensional exactly solvable interacting models are still scarse (see [30,31]).…”

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confidence: 99%

Full counting statistics in the gapped XXZ spin chain

Calabrese

Collura

Giulio

et al. 2020

EPL

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We exploit the knowledge of the entanglement spectrum in the ground state of the gapped XXZ spin chain to derive asymptotic exact results for the full counting statistics of the transverse magnetisation in a large spin block of length . We found that for a subsystem of even length the full counting statistics is Gaussian, while for odd subsystems it is the sum of two Gaussian distributions. We test our analytic predictions with accurate tensor networks simulations. As a byproduct, we also obtain the symmetry (magnetisation) resolved entanglement entropies.

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Exact Local Correlations and Full Counting Statistics for Arbitrary States of the One-Dimensional Interacting Bose Gas

Cited by 93 publications

References 109 publications

Introducing iFluid: a numerical framework for solving hydrodynamical equations in integrable models

Introducing iFluid: a numerical framework for solving hydrodynamical equations in integrable models

Formation probabilities and statistics of observables as defect problems in free fermions and quantum spin chains

Full counting statistics in the gapped XXZ spin chain

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