We consider classical normal modes and noninteracting bosonic excitations in disordered systems. We emphasize generic aspects of such problems and parallels with disordered, noninteracting systems of fermions, and discuss in particular the relevance for bosonic excitations of symmetry classes known in the fermionic context. We also stress important differences between bosonic and fermionic problems. One of these follows from the fact that ground-state stability of a system requires all bosonic excitation energy levels to be positive, while stability in systems of noninteracting fermions is ensured by the exclusion principle, whatever the single-particle energies. As a consequence, simple models of uncorrelated disorder are less useful for bosonic systems than for fermionic ones, and it is generally important to study the excitation spectrum in conjunction with the problem of constructing a disorder-dependent ground state: we show how a mapping to an operator with chiral symmetry provides a useful tool for doing this. A second difference involves the distinction for bosonic systems between excitations which are Goldstone modes and those which are not. In the case of Goldstone modes we review established results illustrating the fact that disorder decouples from excitations in the low-frequency limit, above a critical dimension ${d}_{c},$ which in different circumstances takes the values ${d}_{c}=2$ and ${d}_{c}=0.$ For bosonic excitations which are not Goldstone modes, we argue that an excitation density varying with frequency as $\ensuremath{\rho}(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\omega}}^{4}$ is a universal feature in systems with ground states that depend on the disorder realization. We illustrate our conclusions with extensive analytical and some numerical calculations for a variety of models in one dimension.We consider classical normal modes and noninteracting bosonic excitations in disordered systems. We emphasize generic aspects of such problems and parallels with disordered, noninteracting systems of fermions, and discuss in particular the relevance for bosonic excitations of symmetry classes known in the fermionic context. We also stress important differences between bosonic and fermionic problems. One of these follows from the fact that ground-state stability of a system requires all bosonic excitation energy levels to be positive, while stability in systems of noninteracting fermions is ensured by the exclusion principle, whatever the single-particle energies. As a consequence, simple models of uncorrelated disorder are less useful for bosonic systems than for fermionic ones, and it is generally important to study the excitation spectrum in conjunction with the problem of constructing a disorder-dependent ground state: we show how a mapping to an operator with chiral symmetry provides a useful tool for doing this. A second difference involves the distinction for bosonic systems between excitations which are Goldstone modes and those which are not. In the case of Goldstone modes we review established results illustrating the fact that disorder decouples from excitations in the low-frequency limit, above a critical dimension ${d}_{c},$ which in different circumstances takes the values ${d}_{c}=2$ and ${d}_{c}=0.$ For bosonic excitations which are not Goldstone modes, we argue that an excitation density varying with frequency as $\ensuremath{\rho}(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\omega}}^{4}$ is a universal feature in systems with ground states that depend on the disorder realization. We illustrate our conclusions with extensive analytical and some numerical calculations for a variety of models in one dimension.

arXiv:cond-mat/0305445Physical review. B, Condensed matterOct 15, 2003144 citations

Excitation spectrum for interacting bosons

Kapil M. Khanna, B.K. Das

PhysicaNov 1, 197314 citations

Order by disorder in spin-orbit-coupled Bose-Einstein condensates

Ryan Barnett, Stephen Powell, Tobias Graß +2 more

Motivated by recent experiments, we investigate the system of isotropically interacting bosons with Rashba spin-orbit coupling. At the noninteracting level, there is a macroscopic ground-state degeneracy due to the many ways bosons can occupy the Rashba spectrum. Interactions treated at the mean-field level restrict the possible ground-state configurations, but there remains an accidental degeneracy not corresponding to any symmetry of the Hamiltonian, indicating the importance of fluctuations. By finding analytical expressions for the collective excitations in the long-wavelength limit and through numerical solution of the full Bogoliubov-de Gennes equations, we show that the system condenses into a single-momentum state of the Rashba spectrum via the mechanism of order by disorder. We show that in three dimensions the quantum depletion for this system is small, while the thermal depletion has an infrared logarithmic divergence, which is removed for finite-size systems. In two dimensions, on the other hand, thermal fluctuations destabilize the system.Motivated by recent experiments, we investigate the system of isotropically interacting bosons with Rashba spin-orbit coupling. At the noninteracting level, there is a macroscopic ground-state degeneracy due to the many ways bosons can occupy the Rashba spectrum. Interactions treated at the mean-field level restrict the possible ground-state configurations, but there remains an accidental degeneracy not corresponding to any symmetry of the Hamiltonian, indicating the importance of fluctuations. By finding analytical expressions for the collective excitations in the long-wavelength limit and through numerical solution of the full Bogoliubov-de Gennes equations, we show that the system condenses into a single-momentum state of the Rashba spectrum via the mechanism of order by disorder. We show that in three dimensions the quantum depletion for this system is small, while the thermal depletion has an infrared logarithmic divergence, which is removed for finite-size systems. In two dimensions, on the other hand, thermal fluctuations destabilize the system.

arXiv:1109.4945Physical Review AFeb 13, 201278 citations

Quantum rotor theory of systems of spin-2 bosons

Matjaž Payrits, Ryan Barnett

We consider quantum phases of tightly confined spin-2 bosons in an external field under the presence of rotationally invariant interactions. Generalizing previous treatments, we show how this system can be mapped onto a quantum rotor model. Within the rotor framework, low-energy excitations about fragmented states, which cannot be accessed within standard Bogoliubov theory, can be obtained. In the spatially extended system in the thermodynamic limit there exists a mean field ground-state degeneracy between a family of nematic states for appropriate interaction parameters. It has been established that quantum fluctuations lift this degeneracy through the mechanism of order by disorder and select either a uniaxial or square-biaxial ground state. On the other hand, in the full quantum treatment of the analogous single-spatial-mode problem with finite-particle number, it is known that, due to symmetry-restoring fluctuations, there is a unique ground state across the entire nematic region of the phase diagram. Within the established rotor framework, we investigate the possible quantum phases under the presence of a quadratic Zeeman field, a problem which has previously received little attention. By investigating wave-function overlaps, we do not find any signatures of the order-by-disorder phenomenon which is present in the continuum case. Motivated by this, we consider an alternative external potential which breaks less symmetry than the quadratic Zeeman field. For this case, we do find the phenomenon of order by disorder in the fully quantum system. This is established within the rotor framework and with exact diagonalization.We consider quantum phases of tightly confined spin-2 bosons in an external field under the presence of rotationally invariant interactions. Generalizing previous treatments, we show how this system can be mapped onto a quantum rotor model. Within the rotor framework, low-energy excitations about fragmented states, which cannot be accessed within standard Bogoliubov theory, can be obtained. In the spatially extended system in the thermodynamic limit there exists a mean field ground-state degeneracy between a family of nematic states for appropriate interaction parameters. It has been established that quantum fluctuations lift this degeneracy through the mechanism of order by disorder and select either a uniaxial or square-biaxial ground state. On the other hand, in the full quantum treatment of the analogous single-spatial-mode problem with finite-particle number, it is known that, due to symmetry-restoring fluctuations, there is a unique ground state across the entire nematic region of the phase diagram. Within the established rotor framework, we investigate the possible quantum phases under the presence of a quadratic Zeeman field, a problem which has previously received little attention. By investigating wave-function overlaps, we do not find any signatures of the order-by-disorder phenomenon which is present in the continuum case. Motivated by this, we consider an alternative external potential which breaks less symmetry than the quadratic Zeeman field. For this case, we do find the phenomenon of order by disorder in the fully quantum system. This is established within the rotor framework and with exact diagonalization.

arXiv:1604.05639Physical Review AAug 2, 20162 citations

The Excitation Spectrum for Weakly Interacting Bosons

Robert Seiringer

arXiv:1008.5349Communications in Mathematical PhysicsMay 13, 2011112 citations

{d}_{c},

which in different circumstances takes the values

{d}_{c}=2

and

{d}_{c}=0.

For bosonic excitations which are not Goldstone modes, we argue that an excitation density varying with frequency as $\ensuremath{\rho}(\ensuremath{\omega})\ensuremath{\propto}{\ensuremath{\omega}}^{4}$ is a universal feature in systems with ground states that depend on the disorder realization. We illustrate our conclusions with extensive analytical and some numerical calculations for a variety of models in one dimension.