Critical Behavior of Spin-1/2 One-Dimensional Heisenberg Ferromagnet at Low Temperatures

Yamada, M.; Takahashi, Minoru

doi:10.1143/jpsj.55.2024

Cited by 78 publications

(48 citation statements)

References 22 publications

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“…Apart from the coefficient of t 3/2 in the expansion for C v , the above expressions reproduce precisely the thermodynamic Bethe-ansatz calculations for the spin-1/2 FM Heisenberg chain [45,46]. It is interesting to note that without the factor const in the expression for C v , both expansions fulfill the general hypothesis according to which in 1D Heisenberg ferromagnets all observables should be universal functions of the bare couplings M 0 , s , and h, realizing a no-scale-factor universality [47,48].…”

Section: Thermodynamicssupporting

confidence: 57%

Spin models of quasi-1D quantum ferrimagnets with competing interactions

Ivanov¹

2009

Condens. Matter Phys.

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We present a brief survey of the recent theoretical work related to generic Heisenberg spin models describing quasi-one-dimensional quantum ferrimagnets. The emphasis is on quantum chains and ladders with strong competing interactions, such as the frustrated J 1 − J 2 chain with alternating (1, 1/2) spins, the spin-1/2 diamond chain with four-spin cyclic couplings, and some generic types of mixed-spin ladders with geometric frustration. As a rule, the discussed models exhibit rich quantum phase diagrams and provide some interesting examples of one-dimensional magnetic-paramagnetic quantum phase transitions. A number of open problems in the reviewed research area are discussed.

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Section: Thermodynamicssupporting

confidence: 57%

Spin models of quasi-1D quantum ferrimagnets with competing interactions

Ivanov¹

2009

Condens. Matter Phys.

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“…In these figures, we assumed that the leading correction to the finite-size scaling form is of the form T /J, because the susceptibility for S = 1/2 can be expanded with respect to T /J in the thermodynamic limit. [3,4,6] (This leading correction may vanish in the classical limit as we observe in Fig.1.) We extrapolated the scaling limit quadratically, using the three points nearest to the ordinate.…”

Section: B Analytical Calculation In the Classical Case (S= ∞)mentioning

confidence: 65%

“…For the quantum system, on the other hand, Yamada and Takahashi [3][4][5] employed the Bethe-ansatz method, and numerically obtained the free energy and the zero-field susceptibility of the S = 1/2 ferromagnetic Heisenberg chain in the thermodynamic limit. Their calculations gave critical exponents as α = −1/2, ν = 1 and γ = 2.…”

Section: Introductionmentioning

confidence: 99%

Universal Finite-Size Scaling Function of the Ferromagnetic Heisenberg Chain in a Magnetic Field

1995

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The finite-size scaling function of the magnetization of the ferromagnetic Heisenberg chain is argued to be universal with respect to the magnitude of the spin. The finitesize scaling function is given explicitly by an analytical calculation in the classical limit S = ∞. The universality is checked for S = 1/2 and 1 by means of numerical calculations. Critical exponents are obtained as well. It is concluded that this universal scaling function originates in the universal behavior of the correlation function.

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“…For one, it is extremely hard to solve the infinitely many equations (16) involved in the TBA. Nevertheless, Takahashi and his coworkers [36,51] have given some results for the free energy and susceptibility which are generally accepted. Schlottmann [35] has also predicted the leading order of the specific heat and zero-field susceptibility via analysis of the string solutions to the TBA equations (16).…”

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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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Critical Behavior of Spin-1/2 One-Dimensional Heisenberg Ferromagnet at Low Temperatures

Cited by 78 publications

References 22 publications

Spin models of quasi-1D quantum ferrimagnets with competing interactions

Spin models of quasi-1D quantum ferrimagnets with competing interactions

Universal Finite-Size Scaling Function of the Ferromagnetic Heisenberg Chain in a Magnetic Field

Ferromagnetic behavior in the strongly interacting two-component Bose gas

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