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

Physical review. B, Condensed matter

Bose condensation in quasi-one-dimensional antiferromagnets in strong fields

Ian K. Affleck

Published Feb 1, 1991• 274 citations
Publisher

Abstract

Recent experiments show that axially symmetric integer-spin antiferromagnetic chains undergo a phase transition at a critical applied magnetic field. It was argued, using Landau-Ginzburg theory, that this is one-dimensional Bose condensation. The theory is further analyzed at the mean-field and Gaussian level. Then some exact results concerning the critical behavior are determined using known results on one-dimensional Bose fluids. These are shown to be consistent with recent numerical simulations on spin chains. Breaking of axial symmetry produces crossover to a two-dimensional Ising transition.

DOI
10.1103/physrevb.43.3215

Related papers

Bose-Einstein condensation and critical behavior of two-component bosonic gases

Giacomo Ceccarelli, Jacopo Nespolo, Andrea Pelissetto C +1 more

We study Bose-Einstein condensation (BEC) in three-dimensional two-component bosonic gases, characterizing the universal behaviors of the critical modes arising at the BEC transitions. For this purpose, we use field-theoretical (FT) renormalization-group (RG) methods and perform mean-field and numerical calculations. The FT RG analysis is based on the Landau-Ginzburg-Wilson ${\mathrm{\ensuremath{\Phi}}}^{4}$ theory with two complex scalar fields which has the same symmetry as the bosonic system. In particular, for identical bosons with exchange ${\mathbb{Z}}_{2}$ symmetry, coupled by effective density-density interactions, the global symmetry is ${\mathbb{Z}}_{2,e}\ensuremath{\bigotimes}\mathrm{U}(1)\ensuremath{\bigotimes}\mathrm{U}(1)$. At the BEC transition, it may break into ${\mathbb{Z}}_{2,e}\ensuremath{\bigotimes}{\mathbb{Z}}_{2}\ensuremath{\bigotimes}{\mathbb{Z}}_{2}$ when both components condense simultaneously, or to $\mathrm{U}(1)\ensuremath{\bigotimes}{\mathbb{Z}}_{2}$ when only one component condenses. This implies different universality classes for the corresponding critical behaviors. Numerical simulations of the two-component Bose-Hubbard model in the hard-core limit support the RG prediction: when both components condense simultaneously, the critical behavior is controlled by a decoupled XY fixed point, with unusual slowly decaying scaling corrections arising from the onsite interspecies interaction.

arXiv:1506.04895•Physical Review A•Oct 19, 2015•20 citations

Condensate-induced transitions and critical spin chains

Teresia Månsson, Ville Lahtinen, Juha Suorsa +1 more

We show that condensate-induced transitions between two-dimensional topological phases provide a general framework to relate one-dimensional spin models at their critical points. We demonstrate this using two examples. First, we show that two well-known spin chains, namely, the $\mathit{XY}$ chain and the transverse field Ising chain with only next-nearest-neighbor interactions, differ at their critical points only by a nonlocal boundary term and can be related via an exact mapping. The boundary term constrains the set of possible boundary conditions of the transverse field Ising chain, reducing the number of primary fields in the conformal field theory that describes its critical behavior. We argue that the reduction of the field content is equivalent to the confinement of a set of primary fields, in precise analogy to the confinement of quasiparticles resulting from a condensation of a boson in a topological phase. As the second example we show that when a similar confining boundary term is applied to the $\mathit{XY}$ chain with only next-nearest-neighbor interactions, the resulting system can be mapped to a local spin chain with the $u{(1)}_{2}\ifmmode\times\else\texttimes\fi{}u{(1)}_{2}$ critical behavior predicted by the condensation framework.

arXiv:1212.0351•Physical Review B•Jul 16, 2013•22 citations

Spinor Bose Gases in Cubic Optical lattice

Mohamed Mobarak

In recent years the quantum simulation of condensed-matter physics problems has resulted from ex- citing experimental progress in the realm of ultracold atoms and molecules in optical lattices. In this thesis we analyze theoretically a spinor Bose gas loaded into a three-dimensional cubic optical lattice. In order to account for different superfluid phases of spin-1 bosons with a linear Zeeman effect, we work out a Ginzburg-Landau theory for the underlying spin-1 Bose-Hubbard model. To this end we add artificial symmetry- breaking currents to the spin-1 Bose-Hubbard Hamiltonian in order to break the global U (1) symmetry. With this we determine a diagrammatic expansion of the grand-canonical free energy up to fourth order in the symmetry-breaking currents and up to the leading non-trivial order in the hopping strength which is of first order. As a cross-check we demonstrate that the resulting grand- canonical free energy allows to recover the mean-field theory. Applying a Legendre transfor- mation to the grand-canonical free energy, where the symmetry-breaking currents are transformed to order parameters, we obtain the effective Ginzburg-Landau action. With this we calculate in detail at zero temperature the Mott insulator-superfluid quantum phase boundary as well as condensate and particle number density in the superfluid phase. We find that both mean-field and Ginzburg-Landau theory yield the same quantum phase transition between the Mott insulator and superfluid phases, but the range of validity of the mean-field theory turns out to be smaller than that of the Ginzburg-Landau theory. Due to this finding we expect that the Ginzburg-Landau theory gives better results for the superfluid phase and, thus, we restrict ourselves to extremize only the effective Ginzburg-Landau action with respect to the order parameters. With- out external magnetic field the superfluid phase is a polar (ferromagnetic) state for anti-ferromagnetic (ferromagnetic) interactions, i.e. only the hyperfine spin 0 (1) is macroscopically occupied, in accor- dance with previous mean-field results. On the other hand, in the presence of the external magnetic field for ferromagnetic interaction, the superfluid phase does not change as the minimization of the energy implies the maximal spin value. However, when an anti-ferromagnetic interaction competes with the linear Zeeman effect, we can distinguish various ferromagnetic and anti-ferromagnetic su- perfluid phases within the range of validity of the Ginzburg-Landau theory. Increasing the external magnetic field yields a breaking of spin singlet pairs and a subsequent alignment of spins, thus anti- ferromagnetic phases decrease until only a ferromagnetic superfluid phase prevails. In addition, we find that the superfluid-Mott insulator phase transition is always of second order for both ferromag- netic and anti- ferromagnetic interactions. However, the transitions between different superfluid phases for an anti-ferromagnetic interaction can be both of first and second order depending on whether the respective macroscopic occupation of hyperfine spin states changes discontinuously or continuously. The established Ginzburg-Landau theory for spin-1 bosons in optical lattices will certainly be the basis for many further applications as, for instance, time-of-flight absorption pictures or collective excitations, which are of experimental importance.

•Jan 1, 2014•1 citation

Ginzburg-Landau theory of the zigzag transition in quasi-one-dimensional classical Wigner crystals

J. E. Galván-Moya, François Maria Peeters

We present a mean-field description of the zigzag phase transition of a quasi-one-dimensional system of strongly interacting particles, with interaction potential ${r}^{\ensuremath{-}n}{e}^{\ensuremath{-}r/\ensuremath{\lambda}}$, that are confined by a power-law potential (${y}^{\ensuremath{\alpha}}$). The parameters of the resulting one-dimensional Ginzburg-Landau theory are determined analytically for different values of $\ensuremath{\alpha}$ and $n$. Close to the transition point for the zigzag phase transition, the scaling behavior of the order parameter is determined. For $\ensuremath{\alpha}=2$, the zigzag transition from a single to a double chain is of second order, while for $\ensuremath{\alpha}>2$, the one-chain configuration is always unstable and, for $\ensuremath{\alpha}<2$, the one-chain ordered state becomes unstable at a certain critical density, resulting in jumps of single particles out of the chain.

arXiv:1207.4320•Physical Review B•Oct 18, 2011•18 citations

S=1 antiferromagnetic Heisenberg chain with an axial-symmetry-breaking anisotropy

Tiôru Sakai, Minoru Takahashi

The ground state of the S=1 antiferromagnetic Heisenberg chain with an axial-symmetry-breaking anisotropy ${\mathit{E}\mathit{tsum}}_{\mathit{j}}$ [(${\mathit{S}}_{\mathit{j}}^{\mathit{x}}$${)}^{2}$-(${\mathit{S}}_{\mathit{j}}^{\mathit{y}}$${)}^{2}$] is studied by the finite-size scaling and phenomenological renormalization-group technique based on numerical diagonalizations up to N=14. It is found that two phase transitions exist at ${\mathit{E}}_{\mathit{c}1}$=0.20\ifmmode\pm\else\textpm\fi{}0.01 and ${\mathit{E}}_{\mathit{c}2}$=1.71\ifmmode\pm\else\textpm\fi{}0.01, and both transitions belong to the same universality class as the two-dimensional Ising model.

Physical review. B, Condensed matter•Nov 1, 1991•5 citations

Intrinsic instability at the Bose-Einstein condensation of bosonic quasiparticles in magnetic insulators

A. Schilling

Starting from a phenomenological standard energy functional to describe the condensation of a dilute gas of bosonic quasiparticles in magnetic insulators, we find that the inclusion of a perturbation term that explicitly violates the axial symmetry significantly modifies the details of the resulting Bose Einstein condensation. Systems with an originally axial symmetry must show an intrinsic tendency to spontaneously violate this symmetry as soon as the condensation sets in, and the phase transition at the respective critical field may even become of first order. We can explain a number of features in the experimental data of various insulating spin systems, such as a slightly nonlinear magnetization near the critical field as well as hysteresis effects and peculiarities in the energy-level scheme of TlCuCl3. We also offer a consistent explanation for certain anomalies in the magnetocaloric effect and in the magnetization of BaCuSi2O6 by assuming a spontaneous violation of axial symmetry at the magnetic phase transition on an energy scale of about 1 micro-eV. The resulting anisotropy gap in the magnetic excitation spectrum, that inevitably forms at the critical field of all such systems, lifts the linear Goldstone mode and is therefore seriously limiting the lifetime of magnetic condensates to a few nanoseconds at most.

arXiv:0908.3033•Aug 21, 2009•0 citations
Recent experiments show that axially symmetric integer-spin antiferromagnetic chains undergo a phase transition at a critical applied magnetic field. It was argued, using Landau-Ginzburg theory, that this is one-dimensional Bose condensation. The theory is further analyzed at the mean-field and Gaussian level. Then some exact results concerning the critical behavior are determined using known results on one-dimensional Bose fluids. These are shown to be consistent with recent numerical simulations on spin chains. Breaking of axial symmetry produces crossover to a two-dimensional Ising transition.
We study Bose-Einstein condensation (BEC) in three-dimensional two-component bosonic gases, characterizing the universal behaviors of the critical modes arising at the BEC transitions. For this purpose, we use field-theoretical (FT) renormalization-group (RG) methods and perform mean-field and numerical calculations. The FT RG analysis is based on the Landau-Ginzburg-Wilson ${\mathrm{\ensuremath{\Phi}}}^{4}$ theory with two complex scalar fields which has the same symmetry as the bosonic system. In particular, for identical bosons with exchange Z2{\mathbb{Z}}_{2}Z2​ symmetry, coupled by effective density-density interactions, the global symmetry is ${\mathbb{Z}}_{2,e}\ensuremath{\bigotimes}\mathrm{U}(1)\ensuremath{\bigotimes}\mathrm{U}(1)$. At the BEC transition, it may break into ${\mathbb{Z}}_{2,e}\ensuremath{\bigotimes}{\mathbb{Z}}_{2}\ensuremath{\bigotimes}{\mathbb{Z}}_{2}$ when both components condense simultaneously, or to $\mathrm{U}(1)\ensuremath{\bigotimes}{\mathbb{Z}}_{2}$ when only one component condenses. This implies different universality classes for the corresponding critical behaviors. Numerical simulations of the two-component Bose-Hubbard model in the hard-core limit support the RG prediction: when both components condense simultaneously, the critical behavior is controlled by a decoupled XY fixed point, with unusual slowly decaying scaling corrections arising from the onsite interspecies interaction.
We show that condensate-induced transitions between two-dimensional topological phases provide a general framework to relate one-dimensional spin models at their critical points. We demonstrate this using two examples. First, we show that two well-known spin chains, namely, the XY\mathit{XY}XY chain and the transverse field Ising chain with only next-nearest-neighbor interactions, differ at their critical points only by a nonlocal boundary term and can be related via an exact mapping. The boundary term constrains the set of possible boundary conditions of the transverse field Ising chain, reducing the number of primary fields in the conformal field theory that describes its critical behavior. We argue that the reduction of the field content is equivalent to the confinement of a set of primary fields, in precise analogy to the confinement of quasiparticles resulting from a condensation of a boson in a topological phase. As the second example we show that when a similar confining boundary term is applied to the XY\mathit{XY}XY chain with only next-nearest-neighbor interactions, the resulting system can be mapped to a local spin chain with the $u{(1)}_{2}\ifmmode\times\else\texttimes\fi{}u{(1)}_{2}$ critical behavior predicted by the condensation framework.
In recent years the quantum simulation of condensed-matter physics problems has resulted from ex- citing experimental progress in the realm of ultracold atoms and molecules in optical lattices. In this thesis we analyze theoretically a spinor Bose gas loaded into a three-dimensional cubic optical lattice. In order to account for different superfluid phases of spin-1 bosons with a linear Zeeman effect, we work out a Ginzburg-Landau theory for the underlying spin-1 Bose-Hubbard model. To this end we add artificial symmetry- breaking currents to the spin-1 Bose-Hubbard Hamiltonian in order to break the global U (1) symmetry. With this we determine a diagrammatic expansion of the grand-canonical free energy up to fourth order in the symmetry-breaking currents and up to the leading non-trivial order in the hopping strength which is of first order. As a cross-check we demonstrate that the resulting grand- canonical free energy allows to recover the mean-field theory. Applying a Legendre transfor- mation to the grand-canonical free energy, where the symmetry-breaking currents are transformed to order parameters, we obtain the effective Ginzburg-Landau action. With this we calculate in detail at zero temperature the Mott insulator-superfluid quantum phase boundary as well as condensate and particle number density in the superfluid phase. We find that both mean-field and Ginzburg-Landau theory yield the same quantum phase transition between the Mott insulator and superfluid phases, but the range of validity of the mean-field theory turns out to be smaller than that of the Ginzburg-Landau theory. Due to this finding we expect that the Ginzburg-Landau theory gives better results for the superfluid phase and, thus, we restrict ourselves to extremize only the effective Ginzburg-Landau action with respect to the order parameters. With- out external magnetic field the superfluid phase is a polar (ferromagnetic) state for anti-ferromagnetic (ferromagnetic) interactions, i.e. only the hyperfine spin 0 (1) is macroscopically occupied, in accor- dance with previous mean-field results. On the other hand, in the presence of the external magnetic field for ferromagnetic interaction, the superfluid phase does not change as the minimization of the energy implies the maximal spin value. However, when an anti-ferromagnetic interaction competes with the linear Zeeman effect, we can distinguish various ferromagnetic and anti-ferromagnetic su- perfluid phases within the range of validity of the Ginzburg-Landau theory. Increasing the external magnetic field yields a breaking of spin singlet pairs and a subsequent alignment of spins, thus anti- ferromagnetic phases decrease until only a ferromagnetic superfluid phase prevails. In addition, we find that the superfluid-Mott insulator phase transition is always of second order for both ferromag- netic and anti- ferromagnetic interactions. However, the transitions between different superfluid phases for an anti-ferromagnetic interaction can be both of first and second order depending on whether the respective macroscopic occupation of hyperfine spin states changes discontinuously or continuously. The established Ginzburg-Landau theory for spin-1 bosons in optical lattices will certainly be the basis for many further applications as, for instance, time-of-flight absorption pictures or collective excitations, which are of experimental importance.
We present a mean-field description of the zigzag phase transition of a quasi-one-dimensional system of strongly interacting particles, with interaction potential ${r}^{\ensuremath{-}n}{e}^{\ensuremath{-}r/\ensuremath{\lambda}}$, that are confined by a power-law potential (${y}^{\ensuremath{\alpha}}$). The parameters of the resulting one-dimensional Ginzburg-Landau theory are determined analytically for different values of $\ensuremath{\alpha}$ and nnn. Close to the transition point for the zigzag phase transition, the scaling behavior of the order parameter is determined. For $\ensuremath{\alpha}=2$, the zigzag transition from a single to a double chain is of second order, while for $\ensuremath{\alpha}>2$, the one-chain configuration is always unstable and, for $\ensuremath{\alpha}<2$, the one-chain ordered state becomes unstable at a certain critical density, resulting in jumps of single particles out of the chain.
The ground state of the S=1 antiferromagnetic Heisenberg chain with an axial-symmetry-breaking anisotropy Etsumj{\mathit{E}\mathit{tsum}}_{\mathit{j}}Etsumj​ [(Sjx{\mathit{S}}_{\mathit{j}}^{\mathit{x}}Sjx​)2{)}^{2})2-(Sjy{\mathit{S}}_{\mathit{j}}^{\mathit{y}}Sjy​)2{)}^{2})2] is studied by the finite-size scaling and phenomenological renormalization-group technique based on numerical diagonalizations up to N=14. It is found that two phase transitions exist at Ec1{\mathit{E}}_{\mathit{c}1}Ec1​=0.20\ifmmode\pm\else\textpm\fi{}0.01 and Ec2{\mathit{E}}_{\mathit{c}2}Ec2​=1.71\ifmmode\pm\else\textpm\fi{}0.01, and both transitions belong to the same universality class as the two-dimensional Ising model.
Starting from a phenomenological standard energy functional to describe the condensation of a dilute gas of bosonic quasiparticles in magnetic insulators, we find that the inclusion of a perturbation term that explicitly violates the axial symmetry significantly modifies the details of the resulting Bose Einstein condensation. Systems with an originally axial symmetry must show an intrinsic tendency to spontaneously violate this symmetry as soon as the condensation sets in, and the phase transition at the respective critical field may even become of first order. We can explain a number of features in the experimental data of various insulating spin systems, such as a slightly nonlinear magnetization near the critical field as well as hysteresis effects and peculiarities in the energy-level scheme of TlCuCl3. We also offer a consistent explanation for certain anomalies in the magnetocaloric effect and in the magnetization of BaCuSi2O6 by assuming a spontaneous violation of axial symmetry at the magnetic phase transition on an energy scale of about 1 micro-eV. The resulting anisotropy gap in the magnetic excitation spectrum, that inevitably forms at the critical field of all such systems, lifts the linear Goldstone mode and is therefore seriously limiting the lifetime of magnetic condensates to a few nanoseconds at most.