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Magnetism and quantum phase transitions in spin-1/2 attractive fermions with polarization

He, Jingsong, Angela Foerster, Guan, Xi-Wen, Batchelor, Murray T.

Published Jan 1, 2009• 21 citations
OpenAlex

Abstract

An extensive investigation is given for magnetic properties and phase transitions in one-dimensional (1D) Bethe ansatz integrable spin-1/2 attractive fermions with polarization by means of the dressed energy formalism. An iteration method is presented to derive higher order corrections for the ground-state energy, critical fields and magnetic properties. Numerical solutions of the dressed energy equations confirm that the analytic expressions for these physical quantities and resulting phase diagrams are highly accurate in the weak and strong coupling regimes, capturing the precise nature of magnetic effects and quantum phase transitions in 1D interacting fermions with population imbalance. Moreover, it is shown that the universality class of linear fielddependent behaviour of the magnetization holds throughout the whole attractive regime.

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Magnetism and quantum phase transitions in spin-1/2 attractive fermions with polarization

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An extensive investigation is given for magnetic properties and phase transitions in one-dimensional (1D) Bethe ansatz integrable spin-1/2 attractive fermions with polarization by means of the dressed energy formalism. An iteration method is presented to derive higher order corrections for the ground-state energy, critical fields and magnetic properties. Numerical solutions of the dressed energy equations confirm that the analytic expressions for these physical quantities and resulting phase diagrams are highly accurate in the weak and strong coupling regimes, capturing the precise nature of magnetic effects and quantum phase transitions in 1D interacting fermions with population imbalance. Moreover, it is shown that the universality class of linear field-dependent behaviour of the magnetization holds throughout the whole attractive regime.

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An extensive investigation is given for magnetic properties and phase transitions in one-dimensional (1D) Bethe ansatz integrable spin-1/2 attractive fermions with polarization by means of the dressed energy formalism. An iteration method is presented to derive higher order corrections for the ground-state energy, critical fields and magnetic properties. Numerical solutions of the dressed energy equations confirm that the analytic expressions for these physical quantities and resulting phase diagrams are highly accurate in the weak and strong coupling regimes, capturing the precise nature of magnetic effects and quantum phase transitions in 1D interacting fermions with population imbalance. Moreover, it is shown that the universality class of linear fielddependent behaviour of the magnetization holds throughout the whole attractive regime.
An extensive investigation is given for magnetic properties and phase transitions in one-dimensional (1D) Bethe ansatz integrable spin-1/2 attractive fermions with polarization by means of the dressed energy formalism. An iteration method is presented to derive higher order corrections for the ground-state energy, critical fields and magnetic properties. Numerical solutions of the dressed energy equations confirm that the analytic expressions for these physical quantities and resulting phase diagrams are highly accurate in the weak and strong coupling regimes, capturing the precise nature of magnetic effects and quantum phase transitions in 1D interacting fermions with population imbalance. Moreover, it is shown that the universality class of linear field-dependent behaviour of the magnetization holds throughout the whole attractive regime.
We investigate the ground-state properties of a one-dimensional spin-1/2 fermionic atoms interacting through the attractive δ-function potential in an external magnetic field. By the thermal Bethe ansatz method, the integral equations for the dressed energies are formulated. Those integral equations at zero-temperature are solved in the power series forms of rapidity and momentum for both strong and weak coupling cases. The magnetization as a function of the coupling constant and the external field is also obtained explicitly. Based on the analytic results, quantum phase transitions are identified among three phases, an unpolarized fully paired state, a fully polarized normal ferromagnetic state and a mixed state of paired and unpaired atoms.
We investigate magnetic properties and statistical effects in one-dimensional (1D) strongly repulsive two-component fermions and in a 1D mixture of strongly repulsive polarized fermions and bosons. Universality in the characteristics of phase transitions, magnetization, and susceptibility in the presence of an external magnetic field HHH are analyzed from the exact thermodynamic Bethe ansatz solution. We show explicitly that polarized fermions with a repulsive interaction have antiferromagnetic behavior at zero temperature. A universality class of linear field-dependent magnetization persists for weak and finite strong interaction. The system is fully polarized when the external field exceeds the critical value ${H}_{c}^{F}\ensuremath{\approx}\frac{8}{\ensuremath{\gamma}}{E}_{F}$, where EF{E}_{F}EF​ is the Fermi energy and $\ensuremath{\gamma}$ is the dimensionless interaction strength. In contrast, the mixture of polarized fermions and bosons in an external field exhibits square-root field-dependent magnetization in the vicinities of H=0H=0H=0 and the critical value $H={H}_{c}^{M}\ensuremath{\approx}\frac{16}{\ensuremath{\gamma}}{E}_{F}$. We find that a pure boson phase occurs in the absence of the external field, fully polarized fermions and bosons coexist for 0<H<HcM0<H<{H}_{c}^{M}0<H<HcM​, and a fully polarized fermion phase occurs for $H\ensuremath{\geqslant}{H}_{c}^{M}$. This phase diagram for the Bose-Fermi mixture is reminiscent of weakly attractive fermions with population imbalance, where the interacting fermions with opposite spins form singlet pairs.
We investigate trions, paired states and quantum phase transitions in one-dimensional SU(3) attractive fermions in external fields by means of the Bethe ansatz formalism. Analytical results for the ground state energy, critical fields and complete phase diagrams are obtained for the weak coupling regime. Higher-order corrections for these physical quantities are presented in the strong attractive regime. Numerical solutions of the dressed energy equations allow us to examine how the different phase boundaries are modified by varying the inter-component coupling throughout the whole attractive regime. The pure trionic phase existing in the strong coupling regime decreases smoothly with a decrease in this coupling, until the weak limit is reached. In this weak regime, a pure Bardeen–Cooper–Schrieffer (BCS)-like paired phase can be sustained under certain nonlinear Zeeman splittings.
We investigate trions, paired states and quantum phase transitions in one-dimensional SU(3) attractive fermions in external fields by means of the Bethe ansatz formalism. Analytical results for the ground state energy, critical fields and complete phase diagrams are obtained for the weak coupling regime. Higher-order corrections for these physical quantities are presented in the strong attractive regime. Numerical solutions of the dressed energy equations allow us to examine how the different phase boundaries are modified by varying the intercomponent coupling throughout the whole attractive regime. The pure trionic phase existing in the strong coupling regime decreases smoothly with a decrease in this coupling, until the weak limit is reached. In this weak regime, a pure Bardeen–Cooper–Schrieffer (BCS)-like paired phase can be sustained under certain nonlinear Zeeman splittings.
In this thesis, we present a recent study of the one-dimensional attractively interacting two-component Fermi gas with an external magnetic field. We analytically study the quantum phase diagram, equation of state, quantum criticality, and universal scalings of the model, using the thermodynamic Bethe ansatz equations. We present a high precision equation of state from which universal scaling functions are derived; we show that the thermodynamic properties display universal scaling behaviour at quantum criticality. Expression of high-order-accuracy entropy and specific heat are also analytically derived. Moreover, we present an independent confirmation of the equation of state through an efficient numerical approach of treating the thermodynamic Bethe ansatz equations for which the contributions from the spin strings with length larger than a value of ncn_cnc​ are calculated analytically.