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

arXiv:2310.01570 · Physical review. B./Physical review. B

Magnetization of the antiferromagnetic cactus graph model with an exact dimer ground state

Pratyay Ghosh

Published Dec 14, 2023• 1 citation
arXivHTMLPDF

Abstract

We introduce and explore the magnetization behavior in a quantum spin system on a cactus graph, deemed the cactus graph model, featuring an exact dimer singlet ground state. We analyze the singlet-triplet gap, interactions among excited triplets, and correlated hopping under an external magnetic field using a strong coupling expansion. Employing an effective hard-core boson representation, we unveil density wave magnetization plateaus and supersolid phases, revealing the intricate interplay between interactions and hopping dynamics. Furthermore, we conjecture that correlated hopping gives rise to multitriplet bound states, and potentially engendering to the stabilization of additional low-lying magnetization plateaus.

DOI
10.1103/physrevb.108.214415

Related papers

Maple leaf antiferromagnet in a magnetic field

Pratyay Ghosh, Jannis Seufert, Tobias Müller +2 more

We analyze the quantum antiferromagnet on the maple leaf lattice in the presence of a magnetic field. Starting from its exact dimer ground state and for a magnetic field strength of the order of the local dimer spin-exchange coupling, we perform a strong-coupling expansion and extract an effective hard-core boson model. The interplay of effective many-body interactions, suppressed single-particle dynamics, and correlated hopping gives way to an intriguing series of superfluid to insulator transitions which correspond to magnetization plateaus in terms of the maple leaf spin degrees of freedom. While we find plateaus at intermediate magnetization to be dominated by bosonic density wave order, we conjecture plateau formation from multiboson bound states due to correlated hopping for lower magnetization.

arXiv:2301.08264•Physical review. B./Physical review. B•Aug 29, 2023•21 citations

Magnetization plateaus and jumps in a frustrated four-leg spin tube under a magnetic field

F. A. Gómez Albarracín, Marcelo Arlego, H. D. Rosales

We study the ground state phase diagram of a frustrated spin-1/2 four-leg spin tube in an external magnetic field. We explore the parameter space of this model in the regime of all-antiferromagnetic exchange couplings by means of three different approaches: analysis of low-energy effective Hamiltonian, a Hartree variational approach, and density matrix renormalization group for finite clusters. We find that in the limit of weakly interacting plaquettes, low-energy singlet, triplet, and quintuplet states play an important role in the formation of fractional magnetization plateaus. We study the transition regions numerically and analytically, and find that they are described, at first order in a strong-coupling expansion, by an $XXZ$ spin-1/2 chain in a magnetic field; the second-order terms give corrections to the $XXZ$ model. All techniques provide consistent results which allow us to predict the existence of fractional plateaus in an important region in the space of parameters of the model.

arXiv:1410.5502•Physical Review B•Nov 4, 2014•9 citations

Mechanisms for spin supersolidity in S=12 spin-dimer antiferromagnets

Jean-David Picon, A. Fabricio Albuquerque, Kai Phillip Schmidt +3 more

Using perturbative expansions and the contractor renormalization (CORE) algorithm, we obtain effective hard-core bosonic Hamiltonians describing the low-energy physics of $S=1/2$ spin-dimer antiferromagnets known to display supersolid phases under an applied magnetic field. The resulting effective models are investigated by means of mean-field analysis and quantum Monte Carlo simulations. A ``leapfrog mechanism,'' through means of which extra singlets delocalize in a checkerboard-solid environment via correlated hoppings, is unveiled that accounts for the supersolid behavior.

arXiv:0807.4190•Physical Review B•Nov 17, 2008•24 citations

Interacting spin systems exhibiting spin plateaus and gaps

Bill Sutherland

We study a spin chain and a three-dimensional spin lattice with ground states given by a product of spin-singlet nearest-neighbor pairs. In a magnetic field, the ground state and low-lying states are a mixture of spin singlets and spin-polarized triplets; these states are highly degenerate. When the lattice is distorted, hopping terms are introduced which lift the degeneracy. For particular parameter ranges, the magnetization versus magnetic-field curve exhibits spin plateaus, when the excited states are separated from the ground state by a spin gap. At a critical point, the plateau and the corresponding gap vanish. This spin system is embedded in a more general interacting electron system, and when doped, the charged carriers are found to bind in pairs.

Physical review. B, Condensed matter•Nov 1, 2000•7 citations

Exactly solvable model with spin-triplet pairs and magnetic correlations

Andrei A. Zvyagin, P. Schlottmann

We consider an exactly solvable two-band model of electrons moving in one dimension and interacting with a $\ensuremath{\delta}$-function spin-exchange potential. The relative population of the bands is determined by the band splitting, the magnetic field, and the temperature. The interaction leads to the formation of spin-triplet bound states of the Cooper type (hard-core bosons that do not condensate and exist at all temperatures). In the zero-field ground state the spin-triplet states are effectively free bosons. A threshold band splitting is required to break up a triplet pair. The low-temperature and finite size properties are discussed in the context of anomalous superconducting and antiferromagnetic fluctuations.

Physical review. B, Condensed matter•Sep 1, 1999•6 citations

Magnetization properties of some quantum spin ladders

Kunj Tandon, Siddhartha Lal, Swapan Kumar Pati +2 more

The experimental realization of various spin ladder systems has prompted their detailed theoretical investigations. Here we study the evolution of ground-state magnetization with an external magnetic field for two different antiferromagnetic systems: a three-legged spin-$1/2$ ladder, and a two-legged spin-$1/2$ ladder with an additional diagonal interaction. The finite system density-matrix renormalization-group method is employed for numerical studies of the three-chain system, and an effective low-energy Hamiltonian is used in the limit of strong interchain coupling to study the two- and three-chain systems. The three-chain system has a magnetization plateau at one-third of the saturation magnetization. The two-chain system has a plateau at zero magnetization due to a gap above the singlet ground state. It also has a plateau at half of the saturation magnetization for a certain range of values of the couplings. We study the regions of transitions between plateaus numerically and analytically, and find that they are described, at first order in a strong-coupling expansion, by an $\mathrm{XXZ}$ spin-$1/2$ chain in a magnetic field; the second-order terms give corrections to the $\mathrm{XXZ}$ model. We also study numerically some low-temperature properties of the three-chain system, such as the magnetization, magnetic susceptibility and specific heat.

arXiv:cond-mat/9806111•Physical review. B, Condensed matter•Jan 1, 1999•63 citations
We introduce and explore the magnetization behavior in a quantum spin system on a cactus graph, deemed the cactus graph model, featuring an exact dimer singlet ground state. We analyze the singlet-triplet gap, interactions among excited triplets, and correlated hopping under an external magnetic field using a strong coupling expansion. Employing an effective hard-core boson representation, we unveil density wave magnetization plateaus and supersolid phases, revealing the intricate interplay between interactions and hopping dynamics. Furthermore, we conjecture that correlated hopping gives rise to multitriplet bound states, and potentially engendering to the stabilization of additional low-lying magnetization plateaus.
We analyze the quantum antiferromagnet on the maple leaf lattice in the presence of a magnetic field. Starting from its exact dimer ground state and for a magnetic field strength of the order of the local dimer spin-exchange coupling, we perform a strong-coupling expansion and extract an effective hard-core boson model. The interplay of effective many-body interactions, suppressed single-particle dynamics, and correlated hopping gives way to an intriguing series of superfluid to insulator transitions which correspond to magnetization plateaus in terms of the maple leaf spin degrees of freedom. While we find plateaus at intermediate magnetization to be dominated by bosonic density wave order, we conjecture plateau formation from multiboson bound states due to correlated hopping for lower magnetization.
We study the ground state phase diagram of a frustrated spin-1/2 four-leg spin tube in an external magnetic field. We explore the parameter space of this model in the regime of all-antiferromagnetic exchange couplings by means of three different approaches: analysis of low-energy effective Hamiltonian, a Hartree variational approach, and density matrix renormalization group for finite clusters. We find that in the limit of weakly interacting plaquettes, low-energy singlet, triplet, and quintuplet states play an important role in the formation of fractional magnetization plateaus. We study the transition regions numerically and analytically, and find that they are described, at first order in a strong-coupling expansion, by an XXZXXZXXZ spin-1/2 chain in a magnetic field; the second-order terms give corrections to the XXZXXZXXZ model. All techniques provide consistent results which allow us to predict the existence of fractional plateaus in an important region in the space of parameters of the model.
Using perturbative expansions and the contractor renormalization (CORE) algorithm, we obtain effective hard-core bosonic Hamiltonians describing the low-energy physics of S=1/2S=1/2S=1/2 spin-dimer antiferromagnets known to display supersolid phases under an applied magnetic field. The resulting effective models are investigated by means of mean-field analysis and quantum Monte Carlo simulations. A ``leapfrog mechanism,'' through means of which extra singlets delocalize in a checkerboard-solid environment via correlated hoppings, is unveiled that accounts for the supersolid behavior.
We study a spin chain and a three-dimensional spin lattice with ground states given by a product of spin-singlet nearest-neighbor pairs. In a magnetic field, the ground state and low-lying states are a mixture of spin singlets and spin-polarized triplets; these states are highly degenerate. When the lattice is distorted, hopping terms are introduced which lift the degeneracy. For particular parameter ranges, the magnetization versus magnetic-field curve exhibits spin plateaus, when the excited states are separated from the ground state by a spin gap. At a critical point, the plateau and the corresponding gap vanish. This spin system is embedded in a more general interacting electron system, and when doped, the charged carriers are found to bind in pairs.
We consider an exactly solvable two-band model of electrons moving in one dimension and interacting with a $\ensuremath{\delta}$-function spin-exchange potential. The relative population of the bands is determined by the band splitting, the magnetic field, and the temperature. The interaction leads to the formation of spin-triplet bound states of the Cooper type (hard-core bosons that do not condensate and exist at all temperatures). In the zero-field ground state the spin-triplet states are effectively free bosons. A threshold band splitting is required to break up a triplet pair. The low-temperature and finite size properties are discussed in the context of anomalous superconducting and antiferromagnetic fluctuations.
The experimental realization of various spin ladder systems has prompted their detailed theoretical investigations. Here we study the evolution of ground-state magnetization with an external magnetic field for two different antiferromagnetic systems: a three-legged spin-1/21/21/2 ladder, and a two-legged spin-1/21/21/2 ladder with an additional diagonal interaction. The finite system density-matrix renormalization-group method is employed for numerical studies of the three-chain system, and an effective low-energy Hamiltonian is used in the limit of strong interchain coupling to study the two- and three-chain systems. The three-chain system has a magnetization plateau at one-third of the saturation magnetization. The two-chain system has a plateau at zero magnetization due to a gap above the singlet ground state. It also has a plateau at half of the saturation magnetization for a certain range of values of the couplings. We study the regions of transitions between plateaus numerically and analytically, and find that they are described, at first order in a strong-coupling expansion, by an XXZ\mathrm{XXZ}XXZ spin-1/21/21/2 chain in a magnetic field; the second-order terms give corrections to the XXZ\mathrm{XXZ}XXZ model. We also study numerically some low-temperature properties of the three-chain system, such as the magnetization, magnetic susceptibility and specific heat.