0000000000278162

AUTHOR

J. M. Maillet

showing 6 related works from this author

A form factor approach to the asymptotic behavior of correlation functions in critical models

2011

We propose a form factor approach for the computation of the large distance asymptotic behavior of correlation functions in quantum critical (integrable) models. In the large distance regime we reduce the summation over all excited states to one over the particle/hole excitations lying on the Fermi surface in the thermodynamic limit. We compute these sums, over the so-called critical form factors, exactly. Thus we obtain the leading large distance behavior of each oscillating harmonic of the correlation function asymptotic expansion, including the corresponding amplitudes. Our method is applicable to a wide variety of integrable models and yields precisely the results stemming from the Lutt…

Statistics and ProbabilityHigh Energy Physics - TheoryCritical phenomena[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]FOS: Physical sciences01 natural sciencesBethe ansatzCorrelation functionLuttinger liquid0103 physical sciences[NLIN.NLIN-SI]Nonlinear Sciences [physics]/Exactly Solvable and Integrable Systems [nlin.SI]Statistical physics010306 general physicsCondensed Matter - Statistical MechanicsMathematical PhysicsPhysicsStatistical Mechanics (cond-mat.stat-mech)Nonlinear Sciences - Exactly Solvable and Integrable Systems010308 nuclear & particles physicsConformal field theory[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th]Form factor (quantum field theory)Statistical and Nonlinear PhysicsMathematical Physics (math-ph)16. Peace & justiceHigh Energy Physics - Theory (hep-th)Thermodynamic limitExactly Solvable and Integrable Systems (nlin.SI)Statistics Probability and UncertaintyAsymptotic expansion
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Form factor approach to dynamical correlation functions in critical models

2012

We develop a form factor approach to the study of dynamical correlation functions of quantum integrable models in the critical regime. As an example, we consider the quantum non-linear Schr\"odinger model. We derive long-distance/long-time asymptotic behavior of various two-point functions of this model. We also compute edge exponents and amplitudes characterizing the power-law behavior of dynamical response functions on the particle/hole excitation thresholds. These last results confirm predictions based on the non-linear Luttinger liquid method. Our results rely on a first principles derivation, based on the microscopic analysis of the model, without invoking, at any stage, some correspon…

Statistics and ProbabilityHigh Energy Physics - TheoryIntegrable systemMinor (linear algebra)[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]FOS: Physical sciences01 natural sciencesGapless playbackLuttinger liquid0103 physical sciencesLieb–Liniger model[NLIN.NLIN-SI]Nonlinear Sciences [physics]/Exactly Solvable and Integrable Systems [nlin.SI]Statistical physics010306 general physicsQuantumMathematical PhysicsPhysicsQuantum PhysicsNonlinear Sciences - Exactly Solvable and Integrable Systems010308 nuclear & particles physics[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th]Form factor (quantum field theory)Statistical and Nonlinear PhysicsMathematical Physics (math-ph)AmplitudeHigh Energy Physics - Theory (hep-th)Quantum Gases (cond-mat.quant-gas)Statistics Probability and UncertaintyExactly Solvable and Integrable Systems (nlin.SI)Quantum Physics (quant-ph)Condensed Matter - Quantum Gases
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Open spin chains with generic integrable boundaries: Baxter equation and Bethe ansatz completeness from separation of variables

2014

28 pages; International audience; We solve the longstanding problem to define a functional characterization of the spectrum of the transfer matrix associated to the most general spin-1/2 representations of the 6-vertex reflection algebra for general inhomogeneous chains. The corresponding homogeneous limit reproduces the spectrum of the Hamiltonian of the spin-1/2 open XXZ and XXX quantum chains with the most general integrable boundaries. The spectrum is characterized by a second order finite difference functional equation of Baxter type with an inhomogeneous term which vanishes only for some special but yet interesting non-diagonal boundary conditions. This functional equation is shown to…

Statistics and ProbabilityPhysicsIntegrable system010308 nuclear & particles physics[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th][PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]Finite differenceSeparation of variablesStatistical and Nonlinear Physics01 natural sciencesTransfer matrixBethe ansatzsymbols.namesake0103 physical sciencessymbols[NLIN.NLIN-SI]Nonlinear Sciences [physics]/Exactly Solvable and Integrable Systems [nlin.SI]Boundary value problemStatistics Probability and Uncertainty010306 general physicsHamiltonian (quantum mechanics)QuantumMathematical physics
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Microscopic approach to a class of 1D quantum critical models

2015

Starting from the finite volume form factors of local operators, we show how and under which hypothesis the $c=1$ free boson conformal field theory in two-dimensions emerges as an effective theory governing the large-distance regime of multi-point correlation functions in a large class of one dimensional massless quantum Hamiltonians. In our approach, in the large-distance critical regime, the local operators of the initial model are represented by well suited vertex operators associated to the free boson model. This provides an effective field theoretic description of the large distance behaviour of correlation functions in 1D quantum critical models. We develop this description starting f…

Statistics and ProbabilityPhysicsClass (set theory)Finite volume methodStatistical Mechanics (cond-mat.stat-mech)Field (physics)Nonlinear Sciences - Exactly Solvable and Integrable SystemsConformal field theory[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th][PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]FOS: Physical sciencesGeneral Physics and AstronomyStatistical and Nonlinear PhysicsMathematical Physics (math-ph)Matrix (mathematics)Theoretical physicsModeling and SimulationEffective field theory[NLIN.NLIN-SI]Nonlinear Sciences [physics]/Exactly Solvable and Integrable Systems [nlin.SI]Exactly Solvable and Integrable Systems (nlin.SI)QuantumMathematical PhysicsCondensed Matter - Statistical MechanicsBoson
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Large-distance asymptotic behaviour of multi-point correlation functions in massless quantum models

2014

We provide a microscopic model setting that allows us to readily access to the large-distance asymptotic behaviour of multi-point correlation functions in massless, one-dimensional, quantum models. The method of analysis we propose is based on the form factor expansion of the correlation functions and does not build on any field theory reasonings. It constitutes an extension of the restricted sum techniques leading to the large-distance asymptotic behaviour of two-point correlation functions obtained previously.

Statistics and Probability[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]FOS: Physical sciences01 natural sciencesCorrelation0103 physical sciencesField theory (psychology)[NLIN.NLIN-SI]Nonlinear Sciences [physics]/Exactly Solvable and Integrable Systems [nlin.SI]Statistical physics010306 general physicsQuantumMathematical PhysicsCondensed Matter - Statistical MechanicsMulti pointPhysicsNonlinear Sciences - Exactly Solvable and Integrable SystemsStatistical Mechanics (cond-mat.stat-mech)010308 nuclear & particles physics[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th]Form factor (quantum field theory)Statistical and Nonlinear PhysicsMathematical Physics (math-ph)Method of analysisExtension (predicate logic)Massless particleExactly Solvable and Integrable Systems (nlin.SI)Statistics Probability and Uncertainty
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Thermodynamic limit of particle-hole form factors in the massless XXZ Heisenberg chain

2010

We study the thermodynamic limit of the particle-hole form factors of the XXZ Heisenberg chain in the massless regime. We show that, in this limit, such form factors decrease as an explicitly computed power-law in the system-size. Moreover, the corresponding amplitudes can be obtained as a product of a "smooth" and a "discrete" part: the former depends continuously on the rapidities of the particles and holes, whereas the latter has an additional explicit dependence on the set of integer numbers that label each excited state in the associated logarithmic Bethe equations. We also show that special form factors corresponding to zero-energy excitations lying on the Fermi surface decrease as a …

Statistics and ProbabilityHigh Energy Physics - Theory[NLIN.NLIN-SI] Nonlinear Sciences [physics]/Exactly Solvable and Integrable Systems [nlin.SI]LogarithmIntegrable systemfacteurs de formemodèles intégrables[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]FOS: Physical sciences01 natural sciencesPower law[ PHYS.HTHE ] Physics [physics]/High Energy Physics - Theory [hep-th][PHYS.COND.CM-SM] Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech]Chain (algebraic topology)[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]0103 physical sciencesddc:550[NLIN.NLIN-SI]Nonlinear Sciences [physics]/Exactly Solvable and Integrable Systems [nlin.SI]Limit (mathematics)[MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph][PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech]010306 general physicsMathematical PhysicsCondensed Matter - Statistical MechanicsMathematical physicsPhysicsNonlinear Sciences - Exactly Solvable and Integrable SystemsStatistical Mechanics (cond-mat.stat-mech)010308 nuclear & particles physics[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th][ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph]Statistical and Nonlinear PhysicsMathematical Physics (math-ph)[PHYS.MPHY] Physics [physics]/Mathematical Physics [math-ph]Massless particleHigh Energy Physics - Theory (hep-th)[ PHYS.COND.CM-SM ] Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech]Thermodynamic limitfonctions de corélation[PHYS.HTHE] Physics [physics]/High Energy Physics - Theory [hep-th][ PHYS.MPHY ] Physics [physics]/Mathematical Physics [math-ph]Statistics Probability and UncertaintyExactly Solvable and Integrable Systems (nlin.SI)Critical exponent[ NLIN.NLIN-SI ] Nonlinear Sciences [physics]/Exactly Solvable and Integrable Systems [nlin.SI]
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