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

Journal of Physics Conference Series

Quantum magnetism in spin-3/2 chains

Jhon James Hernández-Sarria, Arturo Argüelles, Karen Rodríguez

Published Jul 3, 2015• 3 citations
Publisher

Abstract

Herein, we characterize the quantum phases present in spin-3/2 fermionic chains. This system may be achieved by ultracold gases loaded onto one-dimentional optical lattices in the hard-core regime. The physics of the lowest band in general is described by the Hubbard Hamiltonian that becomes a generalized Heisenberg model in this strongly-correlated regime. By performing calculations of the energy spectrum, correlation functions, level spectroscopy and chirality we analyze the Mott-insulator phases in absence and presence of an external quadratic Zeeman field.

DOI
10.1088/1742-6596/614/1/012005

Related papers

Mott-Insulator Phases of Spin- 3/2 Fermions in the Presence of Quadratic Zeeman Coupling

Karen Rodríguez, Arturo Argüelles, Maria Colomé‐Tatché +2 more

We study the influence of the quadratic Zeeman effect on the Mott-insulator phases of hard-core 1D spin-3/2 fermions. We show that, contrary to spinor bosons, the quadratic Zeeman coupling preserves an SU(2)⊗SU(2) symmetry, leading for large-enough quadratic Zeeman coupling to an isotropic pseudo-spin-1/2 Heisenberg antiferromagnet. Decreasing the quadratic Zeeman coupling, this phase undergoes, depending on the scattering lengths, either a Kosterlitz-Thouless transition into a gapped dimerized phase or a commensurate-incommensurate transition into a gapless spin liquid. This rich phase diagram can be observed experimentally in four-component fermions in optical lattices under similar entropy constraints to those needed for Néel order in spin-1/2 gases.

arXiv:1002.0287•Physical Review Letters•Jul 27, 2010•22 citations

Magnetic phase transition in coherently coupled Bose gases in optical lattices

Luca Barbiero, Marta Abad, Alessio Recati

We describe the ground state of a gas of bosonic atoms with two coherently coupled internal levels in a deep optical lattice in a one-dimensional geometry. In the single-band approximation this system is described by a Bose-Hubbard Hamiltonian. The system has a superfluid and a Mott insulating phase that can be either paramagnetic or ferromagnetic. We characterize the quantum phase transitions at unit filling by means of a density-matrix renormalization-group technique and compare the results with a mean-field approach and an effective spin Hamiltonian. The presence of the ferromagnetic Ising-like transition modifies the Mott lobes. In the Mott insulating region the system maps to the ferromagnetic spin-1/2 $XXZ$ model in a transverse field and the numerical results compare very well with the analytical results obtained from the spin model. In the superfluid regime quantum fluctuations strongly modify the phase transition with respect to the well-established mean-field three-dimensional classical bifurcation.

arXiv:1403.4185•Physical Review A•Mar 25, 2016•11 citations

Magnon-like properties of 1D spin-3/2 chains

Jhon James Hernández-Sarria, Karen Rodríguez

We study the magnon-like properties of the repulsively interacting spin-3/2 fermions in one-dimensional optical lattices at quarter filling. By means of the Holstein-Primakoff transformation performed on the spinor chain we obtain a spinless boson system described by an extended Bose-Hubbard model with a hole-like lowest band. The magnon model involves single, pair and correlated hopping between nearest neighbors beside the on-site and nearest neighbor interactions. The Mott-insulator phases of the spin-3/2 lattice fermions are mirrored with the magnon-like counterpart by analyzing several observables which should reveal these phases in state-of-the-art experiments. The numerical calculations are performed using the Exact Diagonalization and Matrix Product State formalism.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Aug 25, 2015•0 citations

Fermi-Hubbard Physics with Atoms in an Optical Lattice

Tilman Esslinger

The Fermi-Hubbard model is a key concept in condensed matter physics and provides crucial insights into electronic and magnetic properties of materials. Yet, the intricate nature of Fermi systems poses a barrier to answering important questions concerning d-wave superconductivity and quantum magnetism. Recently, it has become possible to experimentally realize the Fermi-Hubbard model using a fermionic quantum gas loaded into an optical lattice. In this atomic approach to the Fermi-Hubbard model, the Hamiltonian is a direct result of the optical lattice potential created by interfering laser fields and short-ranged ultracold collisions. It provides a route to simulate the physics of the Hamiltonian and to address open questions and novel challenges of the underlying many-body system. This review gives an overview of the current efforts in understanding and realizing experiments with fermionic atoms in optical lattices and discusses key experiments in the metallic, band-insulating, superfluid, and Mott-insulating regimes.

arXiv:1007.0012•Annual Review of Condensed Matter Physics•Jul 29, 2010•569 citations

Strongly Correlated Quantum Phases of Ultracold Atoms in Optical Lattices

Immanuel Bloch

Ultracold quantum gases in optical lattices form almost ideal conditions to analyze the physics of strongly correlated quantum phases in periodic potentials. Such strongly correlated quantum phases are of fundamental interest in condensed matter physics, because they lie at the heart of topical quantum materials, such as high-Tc superconductors and quantum magnets, which pose a challenge to our basic understanding of interacting many-body systems. Quite generally, such strongly interacting quantum phases arise when the interaction energy between two particles dominates over the kinetic energy of the two particles. Such a regime can either be achieved by increasing the interaction strength between the atoms via Feshbach resonances or by decreasing the kinetic energy, such that eventually the interaction energy is the largest energy scale in the system. The latter can, for example, simply be achieved by increasing the optical lattice depth. This chapter tries gives an introduction into the field of optical lattices and the physics of strongly interacting quantum phases. A prominent example hereof is the superfluid-to-Mott insulator transition, which transforms a weakly interacting quantum gas into a strongly correlated many body system. Dominating interactions between the particles are in fact crucial for the Mott insulator transition and also for the realization of controlled interaction-based quantum gates, of which several have been successfully realized experimentally.

SPIE eBooks•Mar 16, 2010•0 citations

Quantum Simulation of Antiferromagnetic Heisenberg Chain with Gate-Defined Quantum Dots

Cornelis Jacobus van Diepen, Tzu-Kan Hsiao, U. Mukhopadhyay +3 more

Quantum-mechanical correlations of interacting fermions result in the emergence of exotic phases.Magnetic phases naturally arise in the Mott-insulator regime of the Fermi-Hubbard model, where charges are localized and the spin degree of freedom remains.In this regime, the occurrence of phenomena such as resonating valence bonds, frustrated magnetism, and spin liquids is predicted.Quantum systems with engineered Hamiltonians can be used as simulators of such spin physics to provide insights beyond the capabilities of analytical methods and classical computers.To be useful, methods for the preparation of intricate many-body spin states and access to relevant observables are required.Here, we show the quantum simulation of magnetism in the Mott-insulator regime with a linear quantum-dot array.We characterize the energy spectrum for a Heisenberg spin chain, from which we can identify when the conditions for homogeneous exchange couplings are met.Next, we study the multispin coherence with global exchange oscillations in both the singlet and triplet subspace of the Heisenberg Hamiltonian.Last, we adiabatically prepare the low-energy global singlet of the homogeneous spin chain and probe it with two-spin singlettriplet measurements on each nearest-neighbor pair and the correlations therein.The methods and control presented here open new opportunities for the simulation of quantum magnetism benefiting from the flexibility in tuning and layout of gate-defined quantum-dot arrays.

arXiv:2103.08238•Physical Review X•Nov 4, 2021•50 citations
Herein, we characterize the quantum phases present in spin-3/2 fermionic chains. This system may be achieved by ultracold gases loaded onto one-dimentional optical lattices in the hard-core regime. The physics of the lowest band in general is described by the Hubbard Hamiltonian that becomes a generalized Heisenberg model in this strongly-correlated regime. By performing calculations of the energy spectrum, correlation functions, level spectroscopy and chirality we analyze the Mott-insulator phases in absence and presence of an external quadratic Zeeman field.
We study the influence of the quadratic Zeeman effect on the Mott-insulator phases of hard-core 1D spin-3/2 fermions. We show that, contrary to spinor bosons, the quadratic Zeeman coupling preserves an SU(2)⊗SU(2) symmetry, leading for large-enough quadratic Zeeman coupling to an isotropic pseudo-spin-1/2 Heisenberg antiferromagnet. Decreasing the quadratic Zeeman coupling, this phase undergoes, depending on the scattering lengths, either a Kosterlitz-Thouless transition into a gapped dimerized phase or a commensurate-incommensurate transition into a gapless spin liquid. This rich phase diagram can be observed experimentally in four-component fermions in optical lattices under similar entropy constraints to those needed for Néel order in spin-1/2 gases.
We describe the ground state of a gas of bosonic atoms with two coherently coupled internal levels in a deep optical lattice in a one-dimensional geometry. In the single-band approximation this system is described by a Bose-Hubbard Hamiltonian. The system has a superfluid and a Mott insulating phase that can be either paramagnetic or ferromagnetic. We characterize the quantum phase transitions at unit filling by means of a density-matrix renormalization-group technique and compare the results with a mean-field approach and an effective spin Hamiltonian. The presence of the ferromagnetic Ising-like transition modifies the Mott lobes. In the Mott insulating region the system maps to the ferromagnetic spin-1/2 XXZXXZXXZ model in a transverse field and the numerical results compare very well with the analytical results obtained from the spin model. In the superfluid regime quantum fluctuations strongly modify the phase transition with respect to the well-established mean-field three-dimensional classical bifurcation.
We study the magnon-like properties of the repulsively interacting spin-3/2 fermions in one-dimensional optical lattices at quarter filling. By means of the Holstein-Primakoff transformation performed on the spinor chain we obtain a spinless boson system described by an extended Bose-Hubbard model with a hole-like lowest band. The magnon model involves single, pair and correlated hopping between nearest neighbors beside the on-site and nearest neighbor interactions. The Mott-insulator phases of the spin-3/2 lattice fermions are mirrored with the magnon-like counterpart by analyzing several observables which should reveal these phases in state-of-the-art experiments. The numerical calculations are performed using the Exact Diagonalization and Matrix Product State formalism.
The Fermi-Hubbard model is a key concept in condensed matter physics and provides crucial insights into electronic and magnetic properties of materials. Yet, the intricate nature of Fermi systems poses a barrier to answering important questions concerning d-wave superconductivity and quantum magnetism. Recently, it has become possible to experimentally realize the Fermi-Hubbard model using a fermionic quantum gas loaded into an optical lattice. In this atomic approach to the Fermi-Hubbard model, the Hamiltonian is a direct result of the optical lattice potential created by interfering laser fields and short-ranged ultracold collisions. It provides a route to simulate the physics of the Hamiltonian and to address open questions and novel challenges of the underlying many-body system. This review gives an overview of the current efforts in understanding and realizing experiments with fermionic atoms in optical lattices and discusses key experiments in the metallic, band-insulating, superfluid, and Mott-insulating regimes.
Ultracold quantum gases in optical lattices form almost ideal conditions to analyze the physics of strongly correlated quantum phases in periodic potentials. Such strongly correlated quantum phases are of fundamental interest in condensed matter physics, because they lie at the heart of topical quantum materials, such as high-Tc superconductors and quantum magnets, which pose a challenge to our basic understanding of interacting many-body systems. Quite generally, such strongly interacting quantum phases arise when the interaction energy between two particles dominates over the kinetic energy of the two particles. Such a regime can either be achieved by increasing the interaction strength between the atoms via Feshbach resonances or by decreasing the kinetic energy, such that eventually the interaction energy is the largest energy scale in the system. The latter can, for example, simply be achieved by increasing the optical lattice depth. This chapter tries gives an introduction into the field of optical lattices and the physics of strongly interacting quantum phases. A prominent example hereof is the superfluid-to-Mott insulator transition, which transforms a weakly interacting quantum gas into a strongly correlated many body system. Dominating interactions between the particles are in fact crucial for the Mott insulator transition and also for the realization of controlled interaction-based quantum gates, of which several have been successfully realized experimentally.
Quantum-mechanical correlations of interacting fermions result in the emergence of exotic phases.Magnetic phases naturally arise in the Mott-insulator regime of the Fermi-Hubbard model, where charges are localized and the spin degree of freedom remains.In this regime, the occurrence of phenomena such as resonating valence bonds, frustrated magnetism, and spin liquids is predicted.Quantum systems with engineered Hamiltonians can be used as simulators of such spin physics to provide insights beyond the capabilities of analytical methods and classical computers.To be useful, methods for the preparation of intricate many-body spin states and access to relevant observables are required.Here, we show the quantum simulation of magnetism in the Mott-insulator regime with a linear quantum-dot array.We characterize the energy spectrum for a Heisenberg spin chain, from which we can identify when the conditions for homogeneous exchange couplings are met.Next, we study the multispin coherence with global exchange oscillations in both the singlet and triplet subspace of the Heisenberg Hamiltonian.Last, we adiabatically prepare the low-energy global singlet of the homogeneous spin chain and probe it with two-spin singlettriplet measurements on each nearest-neighbor pair and the correlations therein.The methods and control presented here open new opportunities for the simulation of quantum magnetism benefiting from the flexibility in tuning and layout of gate-defined quantum-dot arrays.