arXiv:1111.1617 · Physical Review A

Double symmetry breaking and two-dimensional quantum phase diagram in spin-boson systems

Pierre Nataf, Alexandre Baksic, Cristiano Ciuti

Published Jul 23, 2012• 11 citations

Abstract

The quantum ground-state and excitation properties of two independent chains of pseudospins (two-level systems) interacting with the same bosonic field are theoretically investigated. Each chain is coupled to a different quadrature of the field, leading to two independent symmetry breakings for increasing values of the two collective spin-boson interaction constants ${\ensuremath{\Omega}}_{C}$ and ${\ensuremath{\Omega}}_{I}$. A phase diagram is provided in the plane (${\ensuremath{\Omega}}_{C}$,${\ensuremath{\Omega}}_{I}$), with four phases that can be characterized by the complex bosonic coherence of the ground states and can be manipulated via geometric Berry effects. In particular, when ${\ensuremath{\Omega}}_{C}$ and ${\ensuremath{\Omega}}_{I}$ are both larger than two critical values, the fundamental subspace has a fourfold degeneracy. Finite-size properties are shown for both critical and ultrastrong values of ${\ensuremath{\Omega}}_{C}$ and ${\ensuremath{\Omega}}_{I}$. Possible implementations in superconducting quantum circuits are detailed.

DOI: 10.1103/physreva.86.013832

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arXiv:1111.1617 · Physical Review A

Double symmetry breaking and two-dimensional quantum phase diagram in spin-boson systems

Pierre Nataf, Alexandre Baksic, Cristiano Ciuti

Published Jul 23, 2012• 11 citations

arXiv HTML PDF

Abstract

{\ensuremath{\Omega}}_{C}

and

{\ensuremath{\Omega}}_{I}

. A phase diagram is provided in the plane (

{\ensuremath{\Omega}}_{C}

{\ensuremath{\Omega}}_{I}

), with four phases that can be characterized by the complex bosonic coherence of the ground states and can be manipulated via geometric Berry effects. In particular, when

{\ensuremath{\Omega}}_{C}

and

{\ensuremath{\Omega}}_{I}

are both larger than two critical values, the fundamental subspace has a fourfold degeneracy. Finite-size properties are shown for both critical and ultrastrong values of

{\ensuremath{\Omega}}_{C}

and

{\ensuremath{\Omega}}_{I}

. Possible implementations in superconducting quantum circuits are detailed.

DOI: 10.1103/physreva.86.013832

Related papers

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In this set of lectures, I shall review some recent work on quantum critical phenomena which involve the changes in phase of the ground state of a quantum antiferromagnetic system when external parameters are varied through some critical values. I will also draw analogies between antiferromagnetic phase transitions and chiral phase transitions in lower (particularly 2 + l)-dimensional gauge theories and also some 2+1-dimensional four-fermi theories where chiral symmetry breaking patterns depend on the coupling constants and also the matter and gauge field content of the theory. I will begin by reviewing some arguments that, in the infrared limit, the dynamics of Goldstone bosons in the confining and chiral symmetry breaking phase of 2 + 1 dimensional QCD is identical to the effective spin wave dynamics in 2 dimensional generalized quantum antiferromagnets. I also discuss the possibility that certain quantum critical behaviors in generalized antiferromagnets can be analyzed using the principle of universality and are in the universality class of a particular type of relativistic quantum field theory with gauge and chiral symmetry. I show how the epsilon expansion can be used and argue that, for a large range of symmetry groups and other parameters, the phase transitions are expected to be fluctuation induced first order transitions. For the small range of parameters where they are second order, the epsilon expansion and universality give information about the critical behavior.In this set of lectures, I shall review some recent work on quantum critical phenomena which involve the changes in phase of the ground state of a quantum antiferromagnetic system when external parameters are varied through some critical values. I will also draw analogies between antiferromagnetic phase transitions and chiral phase transitions in lower (particularly 2 + l)-dimensional gauge theories and also some 2+1-dimensional four-fermi theories where chiral symmetry breaking patterns depend on the coupling constants and also the matter and gauge field content of the theory. I will begin by reviewing some arguments that, in the infrared limit, the dynamics of Goldstone bosons in the confining and chiral symmetry breaking phase of 2 + 1 dimensional QCD is identical to the effective spin wave dynamics in 2 dimensional generalized quantum antiferromagnets. I also discuss the possibility that certain quantum critical behaviors in generalized antiferromagnets can be analyzed using the principle of universality and are in the universality class of a particular type of relativistic quantum field theory with gauge and chiral symmetry. I show how the epsilon expansion can be used and argue that, for a large range of symmetry groups and other parameters, the phase transitions are expected to be fluctuation induced first order transitions. For the small range of parameters where they are second order, the epsilon expansion and universality give information about the critical behavior.

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{\ensuremath{\Omega}}_{C}

and

{\ensuremath{\Omega}}_{I}

. A phase diagram is provided in the plane (

{\ensuremath{\Omega}}_{C}

{\ensuremath{\Omega}}_{I}

), with four phases that can be characterized by the complex bosonic coherence of the ground states and can be manipulated via geometric Berry effects. In particular, when

{\ensuremath{\Omega}}_{C}

and

{\ensuremath{\Omega}}_{I}

are both larger than two critical values, the fundamental subspace has a fourfold degeneracy. Finite-size properties are shown for both critical and ultrastrong values of

{\ensuremath{\Omega}}_{C}

and

{\ensuremath{\Omega}}_{I}

. Possible implementations in superconducting quantum circuits are detailed.

1/N

with increasing

N

. For a finite number

N

of two-level systems the quantum phase transition (at zero temperature) is in the same universality class as the single spin-boson model; in the limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$ the system shows mean-field critical behavior independent of the power of the spectral function of the bosonic bath. We also study the influence of a spatial separation of the spins in a bath of bosonic modes with linear dispersion relation on the location and characteristics of the phase transition as well as on correlations between the two-level systems.

We study the ground-state properties of the bond-alternating S=1/2 quantum spin chain whose Hamiltonian is H=

{\mathit{tsum}}_{\mathit{j}}

(

{\mathit{S}}_{2\mathit{j}}^{\mathit{x}}

{\mathit{S}}_{2\mathit{j}+1}^{\mathit{x}}

{\mathit{S}}_{2\mathit{j}}^{\mathit{y}}

{\mathit{S}}_{2\mathit{j}+1}^{\mathit{y}}

+\ensuremath{\lambda}

{\mathit{S}}_{2\mathit{j}}^{\mathit{z}}

{\mathit{S}}_{2\mathit{j}+1}^{\mathit{z}}

) +\ensuremath{\beta}t

{sum}_{\mathit{j}}

${\mathbf{S}}_{2\mathit{j}\mathrm{\ensuremath{-}}1}$\ensuremath{\cdot}

{\mathbf{S}}_{2\mathit{j}}

. When \ensuremath{\beta}=0, the ground state is a collection of local singlets with a finite excitation gap. In the limit of strong ferromagnetic coupling \ensuremath{\beta}\ensuremath{\rightarrow}-\ensuremath{\infty}, this is equivalent to the S=1 XXZ Hamiltonian. It has several ground-state phases in the \ensuremath{\lambda}-\ensuremath{\beta} plane including the Haldane phase which has a finite excitation gap above the ground. They are characterized by a full breakdown, partial breakdowns, and a nonbreakdown of the hidden discrete

{\mathit{Z}}_{2}

\ifmmode\times\else\texttimes\fi{}

{\mathit{Z}}_{2}

symmetry. The ground-state phase diagram is obtained by series expansions.

We study the ground-state phase diagram of two-dimensional two-component (or pseudospin-

\frac{1}{2}

) Bose gases in mutually antiparallel synthetic magnetic fields in the space of the total filling factor and the ratio of the intercomponent coupling ${g}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}$ to the intracomponent coupling

g>0

. This time-reversal-invariant setting represents a bosonic analog of spin Hall systems. Using exact diagonalization, we find that (fractional) quantum spin Hall states composed of a pair of nearly independent quantum Hall states are remarkably robust and persist for ${g}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}$ up to as large as

g

. For ${g}_{\ensuremath{\uparrow}\ensuremath{\downarrow}}=\ensuremath{-}g$, we find the exact many-body ground state in which particles in different spin states form pairs. This gives the exact critical line beyond which the system collapses in the thermodynamic limit.