arXiv:1608.00197 · Physical review. B./Physical review. B

Thermodynamics of a spin- 12 XYZ Heisenberg chain with a Dzyaloshinskii-Moriya interaction

Bin Xi, Shijie Hu, Qiang Luo, Jize Zhao, Xiaoqun Wang

Published Jan 6, 2017• 7 citations

Abstract

We study the thermodynamics of a spin-1/2 XYZ Heisenberg chain with a Dzyaloshinskii-Moriya interaction. This model describes the low-energy behaviors of a one-dimensional two-component bosonic model with a synthetic spin-orbit coupling in the deep insulating region. In the limit ${U}^{\ensuremath{'}}/U\ensuremath{\rightarrow}\ensuremath{\infty}$, where $U$ is the strength of the onsite intracomponent repulsion and ${U}^{\ensuremath{'}}$ is the intercomponent one, we solve our model exactly by Jordan-Wigner transformation, and thus provide a benchmark for our following numerical approach. In other cases, we calculate the entropy and the specific heat numerically by the transfer-matrix renormalization-group method. Their low-temperature behaviors depend crucially on the properties of the zero-temperature phases. A refined ground-state phase diagram is then deduced from their low-temperature behaviors. Our findings offer an alternative way to detect those distinguishable phases experimentally.

DOI: 10.1103/physrevb.95.014405

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arXiv:1608.00197 · Physical review. B./Physical review. B

Thermodynamics of a spin- 12 XYZ Heisenberg chain with a Dzyaloshinskii-Moriya interaction

Bin Xi, Shijie Hu, Qiang Luo, Jize Zhao, Xiaoqun Wang

Published Jan 6, 2017• 7 citations

arXiv HTML PDF

Abstract

{U}^{\ensuremath{'}}/U\ensuremath{\rightarrow}\ensuremath{\infty}

, where

U

is the strength of the onsite intracomponent repulsion and

{U}^{\ensuremath{'}}

is the intercomponent one, we solve our model exactly by Jordan-Wigner transformation, and thus provide a benchmark for our following numerical approach. In other cases, we calculate the entropy and the specific heat numerically by the transfer-matrix renormalization-group method. Their low-temperature behaviors depend crucially on the properties of the zero-temperature phases. A refined ground-state phase diagram is then deduced from their low-temperature behaviors. Our findings offer an alternative way to detect those distinguishable phases experimentally.

DOI: 10.1103/physrevb.95.014405

Related papers

Thermodynamics of one-dimensional spin-orbit-coupled bosonic model in deep insulating region

Bin Xi, Shijie Hu, Qiang Luo +2 more

We study the thermodynamics of an XYZ Heisenberg chain with Dzyaloshinskii-Moriya interaction, which describes the low-energy behaviors of a one-dimensional spin-orbit-coupled bosonic model in the deep insulating region. The entropy and the specific heat are calculated numerically by the quasi-exact transfer-matrix renormalization group. In particular, in the limit $U^\prime/U\rightarrow\infty$ , our model is exactly solvable and thus serves as a benchmark for our numerical method. From our data, we find that for $U^\prime/U>1$ a quantum phase transition between an (anti)ferromagnetic phase and a Tomonaga-Luttinger liquid phase occurs at a finite $\theta$ , while for $U^\prime/U<1$ a transition between a ferromagnetic phase and a paramagnetic phase happens at $\theta=0$ . A refined ground-state phase diagram is then deduced from their low-temperature behaviors. Our findings provide an alternative way to detect those distinguishable phases experimentally.We study the thermodynamics of an XYZ Heisenberg chain with Dzyaloshinskii-Moriya interaction, which describes the low-energy behaviors of a one-dimensional spin-orbit-coupled bosonic model in the deep insulating region. The entropy and the specific heat are calculated numerically by the quasi-exact transfer-matrix renormalization group. In particular, in the limit $U^\prime/U\rightarrow\infty$, our model is exactly solvable and thus serves as a benchmark for our numerical method. From our data, we find that for $U^\prime/U>1$ a quantum phase transition between an (anti)ferromagnetic phase and a Tomonaga-Luttinger liquid phase occurs at a finite $\theta$, while for $U^\prime/U<1$ a transition between a ferromagnetic phase and a paramagnetic phase happens at $\theta=0$. A refined ground-state phase diagram is then deduced from their low-temperature behaviors. Our findings provide an alternative way to detect those distinguishable phases experimentally.

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Using the density-matrix renormalization-group algorithm (DMRG) and a finite-size scaling analysis, we study the properties of the one-dimensional completely-anisotropic spin-1/2 XYZ model with Dzyaloshinsky-Moriya (DM) interactions. The model shows a rich phase diagram: depending on the value of the coupling constants, the system can display different kinds of ferromagnetic order and Luttinger-liquid behavior. Transitions from ferromagnetic to Luttinger-liquid phases are first order. We thoroughly discuss the transition between different ferromagnetic phases, which, in the absence of DM interactions, belongs to the XX universality class. We provide evidence that the DM exchange term turns out to split this critical line into two separated Ising-like transitions and that in between a disordered phase may appear. Our study sheds light on the general problem of strongly-interacting spin-orbit-coupled bosonic gases trapped in an optical lattice and can be used to characterize the topological properties of superconducting nanowires in the presence of an imposed supercurrent and of interactions.Using the density-matrix renormalization-group algorithm (DMRG) and a finite-size scaling analysis, we study the properties of the one-dimensional completely-anisotropic spin-1/2 XYZ model with Dzyaloshinsky-Moriya (DM) interactions. The model shows a rich phase diagram: depending on the value of the coupling constants, the system can display different kinds of ferromagnetic order and Luttinger-liquid behavior. Transitions from ferromagnetic to Luttinger-liquid phases are first order. We thoroughly discuss the transition between different ferromagnetic phases, which, in the absence of DM interactions, belongs to the XX universality class. We provide evidence that the DM exchange term turns out to split this critical line into two separated Ising-like transitions and that in between a disordered phase may appear. Our study sheds light on the general problem of strongly-interacting spin-orbit-coupled bosonic gases trapped in an optical lattice and can be used to characterize the topological properties of superconducting nanowires in the presence of an imposed supercurrent and of interactions.

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Long-range spin chirality dimer order in the Heisenberg chain with modulated Dzyaloshinskii-Moriya interactions

Niko Avalishvili, G. I. Japaridze, G. L. Rossini

The ground-state phase diagram of a spin $S=\frac{1}{2}\phantom{\rule{4pt}{0ex}}\text{XXZ}$ Heisenberg chain with spatially modulated Dzyaloshinskii-Moriya interaction $\mathcal{H}={\ensuremath{\sum}}_{n}{J\left({S}_{n}^{x}{S}_{n+1}^{x}+{S}_{n}^{y}{S}_{n+1}^{y}\right)+{J}_{z}{S}_{n}^{z}{S}_{n+1}^{z}+[{D}_{0}+{(\ensuremath{-}1)}^{n}{D}_{1}]({S}_{n}^{x}{S}_{n+1}^{y}\ensuremath{-}{S}_{n}^{y}{S}_{n+1}^{x})}$ is studied using the continuum-limit bosonization approach and extensive density-matrix renormalization group computations. It is shown that the effective continuum-limit bosonized theory of the model is given by the double-frequency sine-Gordon model (DSG) where the frequencies, i.e., the scaling dimensions of the two competing cosine perturbation terms, depend on the effective anisotropy parameter ${\ensuremath{\gamma}}^{*}={J}_{z}/\sqrt{{J}^{2}+{D}_{0}^{2}+{D}_{1}^{2}}$. Exploring the ground-state properties of the DSG model we show that the zero-temperature phase diagram contains the following four phases: (i) the ferromagnetic phase at ${\ensuremath{\gamma}}^{*}\ensuremath{\le}\ensuremath{-}1$; (ii) the gapless Luttinger-liquid (LL) phase at $\ensuremath{-}1<{\ensuremath{\gamma}}^{*}<{\ensuremath{\gamma}}_{\text{C1}}^{*}=\ensuremath{-}1/\sqrt{2}$; (iii) the gapped composite (C1) phase characterized by coexistence of the long-range-ordered (LRO) dimerization pattern $\ensuremath{\epsilon}\ensuremath{\sim}{(\ensuremath{-}1)}^{n}({\mathbf{S}}_{n}{\mathbf{S}}_{n+1})$ with the LRO alternating spin chirality pattern $\ensuremath{\kappa}\ensuremath{\sim}{(\ensuremath{-}1)}^{n}\left({S}_{n}^{x}{S}_{n+1}^{y}\ensuremath{-}{S}_{n}^{y}{S}_{n+1}^{x}\right)$ at ${\ensuremath{\gamma}}_{\text{C1}}^{*}<{\ensuremath{\gamma}}^{*}<{\ensuremath{\gamma}}_{\text{C2}}^{*}$; and (iv) at ${\ensuremath{\gamma}}^{*}>{\ensuremath{\gamma}}_{\text{C2}}^{*}>1$ the gapped composite (C2) phase characterized in addition to the coexisting spin dimerization and alternating chirality patterns, by the presence of LRO antiferromagnetic order. The transition from the LL to the C1 phase at ${\ensuremath{\gamma}}_{\text{C1}}^{*}$ belongs to the Berezinskii-Kosterlitz-Thouless universality class, while the transition at ${\ensuremath{\gamma}}^{*}={\ensuremath{\gamma}}_{\text{C2}}^{*}$ from C1 to C2 phase is of the Ising type.The ground-state phase diagram of a spin $S=\frac{1}{2}\phantom{\rule{4pt}{0ex}}\text{XXZ}$ Heisenberg chain with spatially modulated Dzyaloshinskii-Moriya interaction $\mathcal{H}={\ensuremath{\sum}}_{n}{J\left({S}_{n}^{x}{S}_{n+1}^{x}+{S}_{n}^{y}{S}_{n+1}^{y}\right)+{J}_{z}{S}_{n}^{z}{S}_{n+1}^{z}+[{D}_{0}+{(\ensuremath{-}1)}^{n}{D}_{1}]({S}_{n}^{x}{S}_{n+1}^{y}\ensuremath{-}{S}_{n}^{y}{S}_{n+1}^{x})}$ is studied using the continuum-limit bosonization approach and extensive density-matrix renormalization group computations. It is shown that the effective continuum-limit bosonized theory of the model is given by the double-frequency sine-Gordon model (DSG) where the frequencies, i.e., the scaling dimensions of the two competing cosine perturbation terms, depend on the effective anisotropy parameter ${\ensuremath{\gamma}}^{*}={J}_{z}/\sqrt{{J}^{2}+{D}_{0}^{2}+{D}_{1}^{2}}$. Exploring the ground-state properties of the DSG model we show that the zero-temperature phase diagram contains the following four phases: (i) the ferromagnetic phase at ${\ensuremath{\gamma}}^{*}\ensuremath{\le}\ensuremath{-}1$; (ii) the gapless Luttinger-liquid (LL) phase at $\ensuremath{-}1<{\ensuremath{\gamma}}^{*}<{\ensuremath{\gamma}}_{\text{C1}}^{*}=\ensuremath{-}1/\sqrt{2}$; (iii) the gapped composite (C1) phase characterized by coexistence of the long-range-ordered (LRO) dimerization pattern $\ensuremath{\epsilon}\ensuremath{\sim}{(\ensuremath{-}1)}^{n}({\mathbf{S}}_{n}{\mathbf{S}}_{n+1})$ with the LRO alternating spin chirality pattern $\ensuremath{\kappa}\ensuremath{\sim}{(\ensuremath{-}1)}^{n}\left({S}_{n}^{x}{S}_{n+1}^{y}\ensuremath{-}{S}_{n}^{y}{S}_{n+1}^{x}\right)$ at ${\ensuremath{\gamma}}_{\text{C1}}^{*}<{\ensuremath{\gamma}}^{*}<{\ensuremath{\gamma}}_{\text{C2}}^{*}$; and (iv) at ${\ensuremath{\gamma}}^{*}>{\ensuremath{\gamma}}_{\text{C2}}^{*}>1$ the gapped composite (C2) phase characterized in addition to the coexisting spin dimerization and alternating chirality patterns, by the presence of LRO antiferromagnetic order. The transition from the LL to the C1 phase at ${\ensuremath{\gamma}}_{\text{C1}}^{*}$ belongs to the Berezinskii-Kosterlitz-Thouless universality class, while the transition at ${\ensuremath{\gamma}}^{*}={\ensuremath{\gamma}}_{\text{C2}}^{*}$ from C1 to C2 phase is of the Ising type.

arXiv:1902.09356Physical review. B./Physical review. BMay 31, 201920 citations

Ground-State Properties of the Spin-1/2 Heisenberg-Ising Bond Alternating Chain with Dzyaloshinskii-Moriya Interaction

Jozef Strečka, Lucia Gálisová, Oleg Derzhko

arXiv:1102.0847Acta Physica Polonica ANov 1, 201015 citations

Induced effects of the Dzyaloshinskii-Moriya interaction on the thermal entanglement in spin-1/2 Heisenberg chains

E. Mehran, S. Mahdavifar, Rouhollah Jafari

The nearest-neighbor spins in the one-dimensional spin-1/2 $XX$ model with the added Dzyaloshinskii-Moriya (DM) interaction are entangled at zero temperature. In the presence of a transverse magnetic field (TF) they remain entangled up to a quantum critical field, ${h}_{c}$ . Using the fermionization technique, we have studied the mutual effect of the DM interaction and a TF on the thermal entanglement (TE) in this model. The critical temperature where the entanglement disappears is specified. It is found that the TE in the finite-temperature neighborhood of the quantum critical field shows a scaling behavior with the critical exponent equal to the critical gap exponent. We also argue that thermodynamical properties like the specific heat and the magnetocaloric effect (instead of the usual internal energy and the magnetization) can detect the mentioned quantum entanglement in solid systems. In addition, we suggest a tactic to find all critical temperatures, which is based on the derivative of the entanglement witness with respect to the temperature.The nearest-neighbor spins in the one-dimensional spin-1/2 $XX$ model with the added Dzyaloshinskii-Moriya (DM) interaction are entangled at zero temperature. In the presence of a transverse magnetic field (TF) they remain entangled up to a quantum critical field, ${h}_{c}$. Using the fermionization technique, we have studied the mutual effect of the DM interaction and a TF on the thermal entanglement (TE) in this model. The critical temperature where the entanglement disappears is specified. It is found that the TE in the finite-temperature neighborhood of the quantum critical field shows a scaling behavior with the critical exponent equal to the critical gap exponent. We also argue that thermodynamical properties like the specific heat and the magnetocaloric effect (instead of the usual internal energy and the magnetization) can detect the mentioned quantum entanglement in solid systems. In addition, we suggest a tactic to find all critical temperatures, which is based on the derivative of the entanglement witness with respect to the temperature.

arXiv:1403.3437Physical Review AApr 8, 201439 citations

{U}^{\ensuremath{'}}/U\ensuremath{\rightarrow}\ensuremath{\infty}

, where

U

is the strength of the onsite intracomponent repulsion and

{U}^{\ensuremath{'}}

U^\prime/U\rightarrow\infty

, our model is exactly solvable and thus serves as a benchmark for our numerical method. From our data, we find that for

U^\prime/U>1

a quantum phase transition between an (anti)ferromagnetic phase and a Tomonaga-Luttinger liquid phase occurs at a finite

\theta

, while for

U^\prime/U<1

a transition between a ferromagnetic phase and a paramagnetic phase happens at

\theta=0

. A refined ground-state phase diagram is then deduced from their low-temperature behaviors. Our findings provide an alternative way to detect those distinguishable phases experimentally.

The thermodynamic properties of a spin

S=1/2

tetrameric Heisenberg antiferromagnetic chain with alternating interactions

{\text{AF}}_{1}{\text{-AF}}_{2}{\text{-AF}}_{1}\text{-F}

(AF and F denote the antiferromagnetic and ferromagnetic couplings, respectively) are studied by means of the transfer-matrix renormalization-group method and Jordan-Wigner transformation. It is found that in the absence of magnetic field, the thermodynamic behaviors are closely related to the gapped low-lying excitations, and a novel structure with three peaks in the temperature dependence of specific heat is unveiled. In a magnetic field, a phase diagram in the temperature-field plane for the couplings satisfying

{J}_{{\text{AF}}_{1}}={J}_{{\text{AF}}_{2}}={J}_{\text{F}}

is obtained, in which various phases are identified. The temperature dependence of thermodynamic quantities including the magnetization, susceptibility, and specific heat are studied to characterize the corresponding phases. It is disclosed that the magnetization has a crossover behavior at low temperature in the Luttinger liquid phase, which is shown falling into the same class as that in the

S=1

Haldane chain. In the plateau regime, the thermodynamic behaviors alter at a certain field, which results from the crossing of two excitation spectra. By means of the fermion mapping, it is uncovered that the system has four spectra from fermion and hole excitations that are responsible for the observed thermodynamic behaviors.

The ground-state phase diagram of a spin

S=\frac{1}{2}\phantom{\rule{4pt}{0ex}}\text{XXZ}

Heisenberg chain with spatially modulated Dzyaloshinskii-Moriya interaction $\mathcal{H}={\ensuremath{\sum}}_{n}{J\left({S}_{n}^{x}{S}_{n+1}^{x}+{S}_{n}^{y}{S}_{n+1}^{y}\right)+{J}_{z}{S}_{n}^{z}{S}_{n+1}^{z}+[{D}_{0}+{(\ensuremath{-}1)}^{n}{D}_{1}]({S}_{n}^{x}{S}_{n+1}^{y}\ensuremath{-}{S}_{n}^{y}{S}_{n+1}^{x})}$ is studied using the continuum-limit bosonization approach and extensive density-matrix renormalization group computations. It is shown that the effective continuum-limit bosonized theory of the model is given by the double-frequency sine-Gordon model (DSG) where the frequencies, i.e., the scaling dimensions of the two competing cosine perturbation terms, depend on the effective anisotropy parameter ${\ensuremath{\gamma}}^{*}={J}_{z}/\sqrt{{J}^{2}+{D}_{0}^{2}+{D}_{1}^{2}}$. Exploring the ground-state properties of the DSG model we show that the zero-temperature phase diagram contains the following four phases: (i) the ferromagnetic phase at ${\ensuremath{\gamma}}^{*}\ensuremath{\le}\ensuremath{-}1$; (ii) the gapless Luttinger-liquid (LL) phase at $\ensuremath{-}1<{\ensuremath{\gamma}}^{*}<{\ensuremath{\gamma}}_{\text{C1}}^{*}=\ensuremath{-}1/\sqrt{2}$; (iii) the gapped composite (C1) phase characterized by coexistence of the long-range-ordered (LRO) dimerization pattern $\ensuremath{\epsilon}\ensuremath{\sim}{(\ensuremath{-}1)}^{n}({\mathbf{S}}_{n}{\mathbf{S}}_{n+1})$ with the LRO alternating spin chirality pattern $\ensuremath{\kappa}\ensuremath{\sim}{(\ensuremath{-}1)}^{n}\left({S}_{n}^{x}{S}_{n+1}^{y}\ensuremath{-}{S}_{n}^{y}{S}_{n+1}^{x}\right)$ at ${\ensuremath{\gamma}}_{\text{C1}}^{*}<{\ensuremath{\gamma}}^{*}<{\ensuremath{\gamma}}_{\text{C2}}^{*}$; and (iv) at ${\ensuremath{\gamma}}^{*}>{\ensuremath{\gamma}}_{\text{C2}}^{*}>1$ the gapped composite (C2) phase characterized in addition to the coexisting spin dimerization and alternating chirality patterns, by the presence of LRO antiferromagnetic order. The transition from the LL to the C1 phase at ${\ensuremath{\gamma}}_{\text{C1}}^{*}$ belongs to the Berezinskii-Kosterlitz-Thouless universality class, while the transition at ${\ensuremath{\gamma}}^{*}={\ensuremath{\gamma}}_{\text{C2}}^{*}$ from C1 to C2 phase is of the Ising type.

The nearest-neighbor spins in the one-dimensional spin-1/2

XX

model with the added Dzyaloshinskii-Moriya (DM) interaction are entangled at zero temperature. In the presence of a transverse magnetic field (TF) they remain entangled up to a quantum critical field,

{h}_{c}

. Using the fermionization technique, we have studied the mutual effect of the DM interaction and a TF on the thermal entanglement (TE) in this model. The critical temperature where the entanglement disappears is specified. It is found that the TE in the finite-temperature neighborhood of the quantum critical field shows a scaling behavior with the critical exponent equal to the critical gap exponent. We also argue that thermodynamical properties like the specific heat and the magnetocaloric effect (instead of the usual internal energy and the magnetization) can detect the mentioned quantum entanglement in solid systems. In addition, we suggest a tactic to find all critical temperatures, which is based on the derivative of the entanglement witness with respect to the temperature.