Quantum phases and phase transitions of Mott insulators

Sachdev, Subir

doi:10.1007/bfb0119599

Cited by 28 publications

(32 citation statements)

References 93 publications

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“…In particular, we didn't include in our Hamiltonian direct longitudinal exchange which can enhance the indirect kinetic exchange or compete with it. We didn't consider the phase transitions between different phases, which may have their own peculiarities as compared to currently studied quantum phase transitions in low-dimensional systems 25 . We also didn't discuss possible lattice distortions, which may accompany dimerization.…”

Section: Discussionmentioning

confidence: 99%

Single-pole ladder at quarter filling

2007

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We study the ground state and excitation spectrum of a quasi one-dimensional nanostructure consisting of a pole and rungs oriented in the opposite directions ("centipede ladder", CL) at quarter filling. The spin and charge excitation spectra are found in the limits of small and large longitudinal hopping t compared to the on-rung hopping rate t ⊥ and exchange coupling I ⊥ . At small t the system with ferromagnetic on-rung exchange demonstrates instability against dimerization. Coherent propagation of charge transfer excitons is possible in this limit. At large t CL behaves like two-orbital Hubbard chain, but the gap opens in the charge excitation spectrum thus reducing the symmetry from SU (4) to SU (2). The spin excitations are always gapless and their dispersion changes from quadratic magnon-like for ferromagnetic on-rung exchange to linear spinon-like for antiferromagnetic on-rung exchange in weak longitudinal hopping limit.

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Section: Discussionmentioning

confidence: 99%

Single-pole ladder at quarter filling

2007

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“…other Condensed Matter systems such as graphene or heavy fermion metals (see [48][49][50][51][52][53]55] for reviews), where no precise understanding of thermal critical phenomena or transport properties is available.…”

Section: Jhep09(2012)011mentioning

confidence: 99%

Higher-derivative scalar-vector-tensor theories: black holes, Galileons, singularity cloaking and holography

Charmousis

Goutéraux

Kiritsis

2012

J. High Energ. Phys.

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We consider a general Kaluza-Klein reduction of a truncated Lovelock theory. We find necessary geometric conditions for the reduction to be consistent. The resulting lower-dimensional theory is a higher derivative scalar-tensor theory, depends on a single real parameter and yields second-order field equations. Due to the presence of higherderivative terms, the theory has multiple applications in modifications of Einstein gravity (Galileon/Horndesky theory) and holography (Einstein-Maxwell-Dilaton theories). We find and analyze charged black hole solutions with planar or curved horizons, both in the 'Einstein' and 'Galileon' frame, with or without cosmological constant. Naked singularities are dressed by a geometric event horizon originating from the higher-derivative terms. The near-horizon region of the near-extremal black hole is unaffected by the presence of the higher derivatives, whether scale invariant or hyperscaling violating. In the latter case, the area law for the entanglement entropy is violated logarithmically, as expected in the presence of a Fermi surface. For negative cosmological constant and planar horizons, thermodynamics and first-order hydrodynamics are derived: the shear viscosity to entropy density ratio does not depend on temperature, as expected from the higher-dimensional scale invariance.

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“…Kk, 71.10.Hf, 11.15.Ha An important topic currently under discussion in condensed matter physics community is the emergence of deconfined quantum critical points in gauge theories of Mott insulators in 2 + 1 dimensions [1,2]. A closely related problem concerns the stability of U (1) spin liquids in 2 + 1 dimensions [3,4].…”

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confidence: 99%

Quantum Electrodynamics in2+1Dimensions, Confinement, and the Stability ofU(1)Spin Liquids

Nogueira¹,

Kleinert²

2005

Phys. Rev. Lett.

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Compact quantum electrodynamics in 2 + 1 dimensions often arises as an effective theory for a Mott insulator, with the Dirac fermions representing the low-energy spinons. An important and controversial issue in this context is whether a deconfinement transition takes place. We perform a renormalization group analysis to show that deconfinement occurs when N > Nc = 36/π 3 ≈ 1.161, where N is the number of fermion replica. For N < Nc, however, there are two stable fixed points separated by a line containing a unstable non-trivial fixed point: a fixed point corresponding to the scaling limit of the non-compact theory, and another one governing the scaling behavior of the compact theory. The string tension associated to the confining interspinon potential is shown to exhibit a universal jump as N → N − c . Our results imply the stability of a spin liquid at the physical value N = 2 for Mott insulators.PACS numbers: 11.10. Kk, 71.10.Hf, 11.15.Ha An important topic currently under discussion in condensed matter physics community is the emergence of deconfined quantum critical points in gauge theories of Mott insulators in 2 + 1 dimensions [1,2]. A closely related problem concerns the stability of U (1) spin liquids in 2 + 1 dimensions [3,4]. In either case, models which are often considered as toy models in the high-energy physics literature are supposed to describe the low-energy properties of real systems in condensed matter physics. For instance, a model that frequently appears in the condensed matter literature is the (2 + 1)-dimensional quantum electrodynamics (QED3) [5,6]. It emerges, for instance, as an effective theory for Mott insulators [7,8,9]. Let us briefly recall how it arises in this context. The Hamiltonian of a SU (N ) Heisenberg antiferromagnet is written in a slave-fermion representation as. The resulting effective theory can be treated as a lattice gauge theory, where the gauge field A ij emerges as the phase of χ ij , i.e., χ ij = χ 0 e iAij , where χ 0 is determined from mean-field theory. The (2 + 1)-dimensional lowenergy effective Lagrangian in imaginary time has the form [4,7,8,9]where each ψ a is a four-component Dirac spinor and F µν = ∂ µ A ν − ∂ ν A µ is the usual field strength tensor. A rough estimate of the bare gauge coupling is given by e 2 0 ∼ χ 4 0 a 3 , where a is the lattice spacing. An anisotropic version of QED3 has also been studied in the context of phase fluctuations in d-wave superconductors [10,11]. A key feature of the QED3 theory of Mott insulators is its parity conservation. In fact, it is possible to introduce two different QED3s, one which conserves parity and one which does not. The latter theory involves two-component spinors, and allows for a chirally-invariant mass term which is not parityinvariant. In such a QED3 theory a Chern-Simons term [12] is generated by fluctuations [13]. The QED3 theory relevant to Mott insulators and d-wave superconductors involves four-component spinors, and does possess chiral symmetry [5,6]. In such a model, the chiral symmetry can ...

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Quantum phases and phase transitions of Mott insulators

Cited by 28 publications

References 93 publications

Single-pole ladder at quarter filling

Single-pole ladder at quarter filling

Higher-derivative scalar-vector-tensor theories: black holes, Galileons, singularity cloaking and holography

Quantum Electrodynamics in2+1Dimensions, Confinement, and the Stability ofU(1)Spin Liquids

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