Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physica Scripta

Quantum phases of the 1D anisotropic spin-1/2 frustrated ferromagnetic model: view point of quantum correlations

F. Khastehdel Fumani, Mostafa Motamedifar, S. Mahdavifar

Published Feb 7, 2020• 5 citations
Publisher

Abstract

Abstract We have studied the ground state phases of the one-dimensional (1D) spin-1/2 anisotropic frustrated ferromagnetic model, using the numerical Lanczos method. We have focused on the quantum correlations as the concurrence and the quantum discord (QD) between the nearest neighbor (NN) and the next-nearest neighbor (NNN) spins. Numerical results show that the Tomonaga-Luttinger liquid (TLL), the even-parity dimer, and the vector chiral phases can be distinguished from each other using the long-distance quantum correlations. Specially, the critical points are explicitly detected in the first derivative of the concurrence between the nearest neighbor spins with respect to the frustration parameter.

DOI
10.1088/1402-4896/ab73d7

Related papers

Quantum corrections of the biquadratic interaction in the 1D spin-1/2 frustrated ferromagnetic systems

Javad Vahedi, S. Mahdavifar

Quantum corrections of the biquadratic interaction in the 1D spin-1/2 frustrated ferromagnetic Heisenberg model are studied. The biquadratic interaction for spin-1/2 chains is eliminated and transformed to the quadratic interaction. Doing a numerical experiment, new insight as to how the classical phases get modified on the inclusion of quantum fluctuations is provided. Observed results suggest the existence of an intermediate region in the ground state phase diagram of the frustrated ferromagnetic spin-1/2 chains with combination of dimer and chiral orders. In addition, from the quantum entanglement view point, differences between quantum phases are also obtained. The nearest neighbor spins never be entangled in the frustrated ferromagnetic chains but are entangled up to the Majumdar-Ghosh point in the frustrated antiferromagnetic chains. On the other hand, the next nearest neighbor spins in the mentioned intermediate region are entangled.

arXiv:1204.2905•Apr 13, 2012•1 citation

Entanglement and quantum correlations in the XX spin-1/2 honeycomb lattice

Sahar Satoori, S. Mahdavifar, Javad Vahedi

The ground state phase diagram of the dimerized spin-1/2 XX honeycomb model in presence of a transverse magnetic field (TF) is known. With the absence of the magnetic field, two quantum phases, namely, the Néel and the dimerized phases have been identified. Moreover, canted Néel and the paramagnetic (PM) phases also emerge by applying the magnetic field. In this paper, using two powerful numerical exact techniques, Lanczos exact diagonalization, and Density matrix renormalization group (DMRG) methods, we study this model by focusing on the quantum correlations, the concurrence, and the quantum discord (QD) among nearest-neighbor spins. We show that the quantum correlations can capture the position of the quantum critical points in the whole range of the ground state phase diagram consistent with previous results. Although the concurrence and the QD are short-range, informative about long-ranged critical correlations. In addition, we address a "magnetic-entanglement" behavior that starts from an entangled field around the saturation field.

arXiv:2204.07708•Scientific Reports•Oct 26, 2022•9 citations

Chiral order of spin-1/2 frustrated quantum spin chains

Takashi Hikihara, Makoto Kaburagi, Hikaru Kawamura

The ordering of the frustrated S = 1/2 XY spin chain with the competing nearest- and next-nearest-neighbor anti-ferromagnetic couplings, J1 and J2, is studied by using the density-matrix renormalization-group method. It is found that besides the well-known spin-fluid and dimer phases the chain exhibits a gapless "chiral" phase characterized by the spontaneous breaking of parity, in which the long-range order parameter is a chirality, κl =SxlSyl+1 – Syl Sxl+1, whereas the spin correlation decays algebraically. The dimer phase is realized for 0.33 [Formula: see text] j = J2/J1 [Formula: see text] 1.26 while the chiral phase is realized for j [Formula: see text] 1.26. PACS No.: 75.25

arXiv:cond-mat/0007095•Canadian Journal of Physics•Jan 1, 2001•7 citations

Two-dimensional frustrated Heisenberg model: Variational study

Д. В. Дмитриев, V. Ya. Krivnov, А. А. Овчинников

The stability of the ferromagnetic phase of the two-dimensional (2D) quantum spin-1/2 model with nearest-neighbor ferro- and next-nearest neighbor antiferromagnetic interactions is studied. It turns out that values of exchange integrals at which the ferromagnetic state becomes unstable with respect to a creation of one and two magnons are different. This difference shows that the classical approximation is inapplicable to the study of the transition from the ferromagnetic to the singlet state in contrast with 1D case. This problem is investigated using a variational function. It is based on the boson representation of spin operators which is different from the Holstein-Primakoff approximation. This allows us to obtain an accurate estimate of the transition point and to study the character of the phase transition.

arXiv:cond-mat/9911491•Physical review. B, Condensed matter•Feb 1, 1997•14 citations

Spin-1/2 Heisenberg antiferromagnet with anisotropic nearest- and next-nearest-neighbor coupling

William J. Massano, Janice D. Prie, Jay D. Mancini

A modified Lanczos method has been used to study the ground-state properties of a frustrated one-dimensional anisotropic Heisenberg antiferromagnet. The ground-state energy as well as all two-particle spin-spin correlation functions are obtained for a 16-site lattice. Both the relative couplings and anisotropies for nearest and next-nearest neighbors are varied.

Physical review. B, Condensed matter•Nov 1, 1992•3 citations

Phase diagrams of two-dimensional frustrated spin systems

Ansgar Kalz

In this work the ordering processes in classical frustrated Ising models and the ground-state behavior of frustrated quantum spin models are investigated. In the first part the phase transition from a high-temperature paramagnetic phase to a antiferromagnetic ground state is analyzed for the square-lattice Ising model with competing antiferromagnetic interactions between nearest- and next-nearest-neighbor spins. In the case of spatially isotropic interactions the phase transition to a collinear state is of special interest. Using Monte-Carlo simulations on finite lattices as well as field-theoretical methods for the continuous model it is shown that depending on the frustration three different sectors can be distinguished that show (i) Ising-universal behavior (ii) Ashkin-Teller-like non-universal behavior (varying critical exponents) and (iii) non-critical first-order behavior. For spatially anisotropic interactions the emergence of an intermediate incommensurate phase is verified by means of Monte-Carlo simulations which has been predicted by earlier mean-field calculations. The nature of this phase is studied analyzing spin-spin correlation functions and its ordering wave-vector reveals a strong temperature and size dependence. In the second part the influence of quantum fluctuations on classical antiferromagnetic ground states are investigated in anisotropic quantum spin-1/2 Heisenberg models with competing interactions. Using quantum Monte-Carlo simulations, exact diagonalization and perturbation theory the ground-state phase diagrams are calculated for a square lattice with nearest- and next-nearest-neighbor interactions and a honeycomb lattice with up to third-nearest-neighbor interactions whereby the fluctuations are chosen to be non-frustrating. For both cases the stability regions of classical magnetic states are identified and an intermediate phase is detected that shows no sign of long-range magnetic order. Further calculations also rule out valence-bond-crystal or topological order for this state, thus a quantum disordered ground state is stabilized in these models.

•Jan 1, 2012•0 citations
Abstract We have studied the ground state phases of the one-dimensional (1D) spin-1/2 anisotropic frustrated ferromagnetic model, using the numerical Lanczos method. We have focused on the quantum correlations as the concurrence and the quantum discord (QD) between the nearest neighbor (NN) and the next-nearest neighbor (NNN) spins. Numerical results show that the Tomonaga-Luttinger liquid (TLL), the even-parity dimer, and the vector chiral phases can be distinguished from each other using the long-distance quantum correlations. Specially, the critical points are explicitly detected in the first derivative of the concurrence between the nearest neighbor spins with respect to the frustration parameter.
Quantum corrections of the biquadratic interaction in the 1D spin-1/2 frustrated ferromagnetic Heisenberg model are studied. The biquadratic interaction for spin-1/2 chains is eliminated and transformed to the quadratic interaction. Doing a numerical experiment, new insight as to how the classical phases get modified on the inclusion of quantum fluctuations is provided. Observed results suggest the existence of an intermediate region in the ground state phase diagram of the frustrated ferromagnetic spin-1/2 chains with combination of dimer and chiral orders. In addition, from the quantum entanglement view point, differences between quantum phases are also obtained. The nearest neighbor spins never be entangled in the frustrated ferromagnetic chains but are entangled up to the Majumdar-Ghosh point in the frustrated antiferromagnetic chains. On the other hand, the next nearest neighbor spins in the mentioned intermediate region are entangled.
The ground state phase diagram of the dimerized spin-1/2 XX honeycomb model in presence of a transverse magnetic field (TF) is known. With the absence of the magnetic field, two quantum phases, namely, the Néel and the dimerized phases have been identified. Moreover, canted Néel and the paramagnetic (PM) phases also emerge by applying the magnetic field. In this paper, using two powerful numerical exact techniques, Lanczos exact diagonalization, and Density matrix renormalization group (DMRG) methods, we study this model by focusing on the quantum correlations, the concurrence, and the quantum discord (QD) among nearest-neighbor spins. We show that the quantum correlations can capture the position of the quantum critical points in the whole range of the ground state phase diagram consistent with previous results. Although the concurrence and the QD are short-range, informative about long-ranged critical correlations. In addition, we address a "magnetic-entanglement" behavior that starts from an entangled field around the saturation field.
The ordering of the frustrated S = 1/2 XY spin chain with the competing nearest- and next-nearest-neighbor anti-ferromagnetic couplings, J1 and J2, is studied by using the density-matrix renormalization-group method. It is found that besides the well-known spin-fluid and dimer phases the chain exhibits a gapless "chiral" phase characterized by the spontaneous breaking of parity, in which the long-range order parameter is a chirality, κl =SxlSyl+1 – Syl Sxl+1, whereas the spin correlation decays algebraically. The dimer phase is realized for 0.33 [Formula: see text] j = J2/J1 [Formula: see text] 1.26 while the chiral phase is realized for j [Formula: see text] 1.26. PACS No.: 75.25
The stability of the ferromagnetic phase of the two-dimensional (2D) quantum spin-1/2 model with nearest-neighbor ferro- and next-nearest neighbor antiferromagnetic interactions is studied. It turns out that values of exchange integrals at which the ferromagnetic state becomes unstable with respect to a creation of one and two magnons are different. This difference shows that the classical approximation is inapplicable to the study of the transition from the ferromagnetic to the singlet state in contrast with 1D case. This problem is investigated using a variational function. It is based on the boson representation of spin operators which is different from the Holstein-Primakoff approximation. This allows us to obtain an accurate estimate of the transition point and to study the character of the phase transition.
In this work the ordering processes in classical frustrated Ising models and the ground-state behavior of frustrated quantum spin models are investigated. In the first part the phase transition from a high-temperature paramagnetic phase to a antiferromagnetic ground state is analyzed for the square-lattice Ising model with competing antiferromagnetic interactions between nearest- and next-nearest-neighbor spins. In the case of spatially isotropic interactions the phase transition to a collinear state is of special interest. Using Monte-Carlo simulations on finite lattices as well as field-theoretical methods for the continuous model it is shown that depending on the frustration three different sectors can be distinguished that show (i) Ising-universal behavior (ii) Ashkin-Teller-like non-universal behavior (varying critical exponents) and (iii) non-critical first-order behavior. For spatially anisotropic interactions the emergence of an intermediate incommensurate phase is verified by means of Monte-Carlo simulations which has been predicted by earlier mean-field calculations. The nature of this phase is studied analyzing spin-spin correlation functions and its ordering wave-vector reveals a strong temperature and size dependence. In the second part the influence of quantum fluctuations on classical antiferromagnetic ground states are investigated in anisotropic quantum spin-1/2 Heisenberg models with competing interactions. Using quantum Monte-Carlo simulations, exact diagonalization and perturbation theory the ground-state phase diagrams are calculated for a square lattice with nearest- and next-nearest-neighbor interactions and a honeycomb lattice with up to third-nearest-neighbor interactions whereby the fluctuations are chosen to be non-frustrating. For both cases the stability regions of classical magnetic states are identified and an intermediate phase is detected that shows no sign of long-range magnetic order. Further calculations also rule out valence-bond-crystal or topological order for this state, thus a quantum disordered ground state is stabilized in these models.