Massive CP1 theory from a microscopic model for doped antiferromagnets

Falb, J.; Muramatsu, A.

doi:10.1016/j.nuclphysb.2007.10.025

“…We note that an application to the fermionic repulsive Hubbard model is complicated by the choice of the qualitative features of the ground state being debatable. In this case, a treatment of the constraint along the lines of [35] (3) δ α1 δ α1 = 2s (3) .…”

Section: Discussionmentioning

confidence: 99%

Quantum field theory for the three-body constrained lattice Bose gas. I. Formal developments

Diehl

¹

,

Baranov

²

,

Daley

³

et al. 2010

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We develop a quantum field theoretical framework to analytically study the three-body constrained Bose-Hubbard model beyond mean field and non-interacting spin wave approximations. It is based on an exact mapping of the constrained model to a theory with two coupled bosonic degrees of freedom with polynomial interactions, which have a natural interpretation as single particles and two-particle states. The procedure can be seen as a proper quantization of the Gutzwiller mean field theory. The theory is conveniently evaluated in the framework of the quantum effective action, for which the usual symmetry principles are now supplemented with a "constraint principle" operative on short distances. We test the theory via investigation of scattering properties of few particles in the limit of vanishing density, and we address the complementary problem in the limit of maximum filling, where the low lying excitations are holes and di-holes on top of the constraint induced insulator. This is the first of a sequence of two papers. The application of the formalism to the many-body problem, which can be realized with atoms in optical lattices with strong three-body loss, is performed in a related work [14].PACS numbers: 03.70.+k,11.15.Me,67.85.Hj I. INTRODUCTIONLattice theories with constrained bosons have proven to be a powerful description of various spin models and strongly correlated systems in condensed matter physics [1]. On the other hand, such theories with constrained lattice bosons have recently arisen naturally in effective models for experiments with cold atoms in optical lattices. In the presence of large two-body and three-body loss processes, bosons in an optical lattice are described on short timescales by a model with two-body and threebody constraints respectively [2,3]. The behavior of the Bose gas is changed drastically; for example, in the case of the three-body constraint, the creation of an attractive Bose gas with atomic (ASF) and dimer superfluid (DSF) phases is possible [3]. While the possibility of such an ASF-DSF transition has been predicted earlier in the context of continuum attractive Bose gases near Feshbach resonances [4,5], the constrained lattice system offers an intrinsic stabilization mechanism to observe such a phenomenology in experiments. This serves as one motivation to study such models theoretically in more detail, in particular exploring the consequences of the presence of the constraint. We also note that by the same dissipative blockade mechanism, constrained models with fermions may be created [6,7].Here our goal is to describe the physics of a constrained boson system beyond a mean-field plus spin wave approach (see e.g. [1]). In order to do this, we find an exact mapping of the original constrained bosonic Hubbard model to a theory of two coupled unconstrained bosonic degrees of freedom which interact polynomially. The resulting theory is conveniently analyzed in the framework of the quantum effective action, which makes it possible to study both thermodynamical and dynami...

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“…It follows from a Renormalization Group analysis based on the results of Refs. 26,27 that for intermediate and large values of U/4t obeying approximately the inequality U/4t ≥ u 0 ≈ 1.302, besides the original nearest-neighboring hoping processes only those involving second and third neighboring sites are relevant for the square-lattice quantum liquid described by the Hamiltonian of Eqs. ( 1) and ( 4) in the one-and two-electron subspace.…”

Section: The Model a Suitable Rotated-electron Description And The Gl...mentioning

confidence: 99%

A description of the Hubbard model on a square lattice consistent with its global $SO(3)\times SO(3)\times U(1)$ symmetry

Carmelo,

Sampaio

2008

Preprint

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In this paper a description of the Hubbard model on the square lattice with nearest-neighbor transfer integral t, on-site repulsion U , and N 2 a ≫ 1 sites consistent with its exact global SO(3) × SO(3) × U (1) symmetry is constructed. Our studies profit from the interplay of that recently found global symmetry of the model on any bipartite lattice with the transformation laws under a suitable electron -rotated-electron unitary transformation of a well-defined set of operators and quantum objects. For U/4t > 0 the occupancy configurations of these objects generate the energy eigenstates that span the one-and two-electron subspace. Such a subspace as defined in this paper contains nearly the whole spectral weight of the excitations generated by application onto the zero-spindensity ground state of one-and two-electron operators. Our description involves three basic objects: charge c fermions, spin-1/2 spinons, and η-spin-1/2 η-spinons. Independent spinons and independent η-spinons are invariant under the above unitary transformation. Alike in chromodynamics the quarks have color but all quark-composite physical particles are color-neutral, the η-spinon (and spinons) that are not invariant under that transformation have η spin 1/2 (and spin 1/2) but are part of η-spinneutral (and spin-neutral) 2ν-η-spinon (and 2ν-spinon) composite ην fermions (and sν fermions) where ν = 1, 2, ... is the number of η-spinon (and spinon) pairs. The occupancy configurations of the c fermions, independent spinons and 2ν-spinon composite sν fermions, and independent η-spinons and 2ν-η-spinon composite ην fermions correspond to the state representations of the U (1), spin SU (2), and η-spin SU (2) symmetries, respectively, associated with the model2 global symmetry. The components of the αν fermion discrete momentum values qj = [qj x1 , qj x2 ] are eigenvalues of the corresponding set of αν translation generators in the presence of fictitious magnetic fields Bαν. Our operator description has been constructed to inherently the αν translation generators ˆ q αν in the presence of the fictitious magnetic field Bαν commuting with the momentum operator, consistently with their component operators qαν x 1 and qαν x 1 commuting with each other. In turn, unlike for the 1D model such generators not commute in general with the Hamiltonian, except for the Hubbard model on the square lattice in the oneand two-electron subspace. Concerning one-and two-electron excitations, the picture that emerges is that of a two-component quantum liquid of charge c fermions and spin-neutral two-spinon s1 fermions. The description introduced here is consistent with a Mott-Hubbard insulating ground state with antiferromagnetic long-range order for half filling at x = 0 hole concentration and a ground state with short-range spin order for a well-defined range of finite hole concentrations x > 0. For 0 < x ≪ 1 the latter short-range spin order has an incomensurate-spiral character. Our results are of interest for studies of ultra-cold fermionic atoms on optical lattices ...

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“…We note that an application to the fermionic repulsive Hubbard model is complicated by the choice of the qualitative features of the ground state being debatable. In this case, a treatment of the constraint along the lines of [35] may be preferrable. q 1 p 1 (ω) 1 p 1 (−ω) 1 2 [ q 3 −q + q+q 3 −q 4 + q 1 −q + q+q 1 −q 4 ][ q−q 4 + q ] + {q 3 ↔ q 4 , q 1 → q 2 } − q,q 1 p 1 (ω)…”

Section: Discussionmentioning

confidence: 99%

Quantum Field Theory for the Three-Body Constrained Lattice Bose Gas -- Part I: Formal Developments

Diehl,

Baranov,

Daley

et al. 2009

Preprint

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We develop a quantum field theoretical framework to analytically study the three-body constrained Bose-Hubbard model beyond mean field and non-interacting spin wave approximations. It is based on an exact mapping of the constrained model to a theory with two coupled bosonic degrees of freedom with polynomial interactions, which have a natural interpretation as single particles and two-particle states. The procedure can be seen as a proper quantization of the Gutzwiller mean field theory. The theory is conveniently evaluated in the framework of the quantum effective action, for which the usual symmetry principles are now supplemented with a "constraint principle" operative on short distances. We test the theory via investigation of scattering properties of few particles in the limit of vanishing density, and we address the complementary problem in the limit of maximum filling, where the low lying excitations are holes and di-holes on top of the constraint induced insulator. This is the first of a sequence of two papers. The application of the formalism to the many-body problem, which can be realized with atoms in optical lattices with strong three-body loss, is performed in a related work [14].

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Massive CP1 theory from a microscopic model for doped antiferromagnets

Cited by 8 publications

References 50 publications

Quantum field theory for the three-body constrained lattice Bose gas. I. Formal developments

Quantum field theory for the three-body constrained lattice Bose gas. I. Formal developments

A description of the Hubbard model on a square lattice consistent with its global $SO(3)\times SO(3)\times U(1)$ symmetry

Quantum Field Theory for the Three-Body Constrained Lattice Bose Gas -- Part I: Formal Developments

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