String correlation functions of the spin-1/2 Heisenberg<i>XXZ</i>chain

Bortz, Michael; Sato, Jun; Shiroishi, Masahiro

doi:10.1088/1751-8113/40/16/001

Cited by 23 publications

(25 citation statements)

References 49 publications

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“…For C string (x), this constant vanishes only in the critical phase. It is non-zero when the fermion mass is a relevant coupling in the field theory, corresponding to the appearance of the string order induced by the staggered magnetic field in the spin model [16,17]. This property is also seen in numerical results of this work.…”

Section: Numerical Results For the Phase Structure Of The Massive Thisupporting

confidence: 61%

Phase structure and real-time dynamics of the massive Thirring model in 1+1 dimensions using the tensor-network method

Bañuls¹,

Cichy²,

Hung³

et al. 2020

Proceedings of 37th International Symposium on Lattice Field Theory — PoS(LATTICE2019)

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We present concluding results from our study for zero-temperature phase structure of the massive Thirring model in 1+1 dimensions with staggered regularisation. Employing the method of matrix product states, several quantities, including two types of correlators, are investigated, leading to numerical evidence of a Berezinskii-Kosterlitz-Thouless phase transition. Exploratory results for real-time dynamics pertaining to this transition, obtained using the approaches of variational uniform matrix product state and time-dependent variational principle, are also discussed.

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Section: Numerical Results For the Phase Structure Of The Massive Thisupporting

confidence: 61%

Phase structure and real-time dynamics of the massive Thirring model in 1+1 dimensions using the tensor-network method

Bañuls¹,

Cichy²,

Hung³

et al. 2020

Proceedings of 37th International Symposium on Lattice Field Theory — PoS(LATTICE2019)

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“…For ℓ → ∞ the determinant (2.53) can be evaluated using the generalized Fisher-Hartwig conjecture for Toeplitz determinants to obtain the result (we assume λ < π since we desire the derivatives at λ = 0 for the cumulants) [87] (see also Ref. [88])…”

Section: The Spin-1/2 XX Chainmentioning

confidence: 99%

Bipartite fluctuations as a probe of many-body entanglement

et al. 2012

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We investigate in detail the behavior of the bipartite fluctuations of particle numberN and spin S z in many-body quantum systems, focusing on systems where such U(1) charges are both conserved and fluctuate within subsystems due to exchange of charges between subsystems. We propose that the bipartite fluctuations are an effective tool for studying many-body physics, particularly its entanglement properties, in the same way that noise and Full Counting Statistics have been used in mesoscopic transport and cold atomic gases. For systems that can be mapped to a problem of non-interacting fermions we show that the fluctuations and higher-order cumulants fully encode the information needed to determine the entanglement entropy as well as the full entanglement spectrum through the Rényi entropies. In this connection we derive a simple formula that explicitly relates the eigenvalues of the reduced density matrix to the Rényi entropies of integer order for any finite density matrix. In other systems, particularly in one dimension, the fluctuations are in many ways similar but not equivalent to the entanglement entropy. Fluctuations are tractable analytically, computable numerically in both density matrix renormalization group and quantum Monte Carlo calculations, and in principle accessible in condensed matter and cold atom experiments. In the context of quantum point contacts, measurement of the second charge cumulant showing a logarithmic dependence on time would constitute a strong indication of many-body entanglement.

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“…The upper set of curves are obtained from the spinor Bose gas specific heat (44). The lower set of curves follow from the spinless Bose gas result (37).…”

Section: Fig 4: (Color Online)mentioning

confidence: 99%

Ferromagnetic behavior in the strongly interacting two-component Bose gas

2007

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We investigate the low temperature behaviour of the integrable 1D two-component spinor Bose gas using the thermodynamic Bethe ansatz. We find that for strong coupling the characteristics of the thermodynamics at low temperatures are quantitatively affected by the spin ferromagnetic states, which are described by an effective ferromagnetic Heisenberg chain. The free energy, specific heat, susceptibility and local pair correlation function are calculated for various physical regimes in terms of temperature and interaction strength. These thermodynamic properties reveal spin effects which are significantly different than those of the spinless Bose gas. The zero-field susceptibility for finite strong repulsion exceeds that of a free spin paramagnet. The critical exponents of the specific heat cv ∼ T 1/2 and the susceptibility χ ∼ T −2 are indicative of the ferromagnetic signature of the two-component spinor Bose gas. Our analytic results are consistent with general arguments by Eisenberg and Lieb for polarized spinor bosons.PACS numbers: 03.75. Hh, 03.75.Mn, 04.20.Jb, 05.30.Jp I. INTRODUCTIONExperiments with ultracold quantum gases are opening up exciting new possibilities for testing and exploring quantum effects in many-body systems (for recent reviews, see Refs. [1][2][3]). These include experiments on effectively one-dimensional (1D) quantum Bose gases of 87 Rb atoms in which the interaction strength between atoms is tunable [4][5][6][7][8]. The experiments provide a striking example of realizing an integrable quantum many-body problem. They demonstrate the explicit fermionization of bosons and provide a direct test of theoretical results obtained for the integrable 1D interacting (spinless) Bose gas [9,10]. Another frontier of activity involves spinor Bose gases of alkali atoms in which hyperfine states comprise the pseudospins [11][12][13]. In these systems quantum collisional effects can produce spatio-temporal spin oscillations (spin waves) [14][15][16][17]. The observation of collective dynamics of spin waves and spin-state segregation in trapped spinor Bose gases has stimulated a wide range of interest in studying magnetism, topological spin defects and novel quantum phase transitions in spinor Bose gases [18,19]. Two-component spinor Bose gases have been experimentally created in a magnetic trap by rotating two hyperfine states so that the two atomic hyperfine states make up a pseudo-spin doublet [20], e.g., the |F = 2, m F = −1 and |F = 1, m F = 1 hyperfine states of 87 Rb. In general, spin-independent s-wave scattering dominates interactions in alkali atomic gases. In 1D, the two-component Bose gas with spin-independent s-wave scattering can be exactly solved, like the spinless model, by means of the Bethe ansatz [21,22]. In contrast to Fermi gases, ferromagnetic order emerges in spinor Bose gases as long as the interaction is fully spin independent [15,23]. The low-energy excitations of the model split into collective excitations carrying charge and collective excitations carrying spin. The charge...

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String correlation functions of the spin-1/2 HeisenbergXXZchain

Cited by 23 publications

References 49 publications

Phase structure and real-time dynamics of the massive Thirring model in 1+1 dimensions using the tensor-network method

Phase structure and real-time dynamics of the massive Thirring model in 1+1 dimensions using the tensor-network method

Bipartite fluctuations as a probe of many-body entanglement

Ferromagnetic behavior in the strongly interacting two-component Bose gas

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