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Publications (10 of 39) Show all publications
Langmann, E. & Moosavi, P. (2019). Diffusive Heat Waves in Random Conformal Field Theory. Physical Review Letters, 122(2), Article ID 020201.
Open this publication in new window or tab >>Diffusive Heat Waves in Random Conformal Field Theory
2019 (English)In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 122, no 2, article id 020201Article in journal (Refereed) Published
Abstract [en]

We propose and study a conformal field theory (CFT) model with random position-dependent velocity that, as we argue, naturally emerges as an effective description of heat transport in one-dimensional quantum many-body systems with certain static random impurities. We present exact analytical results that elucidate how purely ballistic heat waves in standard CFT can acquire normal and anomalous diffusive contributions due to our impurities. Our results include impurity-averaged Green's functions describing the time evolution of the energy density and the heat current, and an explicit formula for the thermal conductivity that, in addition to a universal Drude peak, has a nontrivial real regular contribution that depends on details of the impurities.

Place, publisher, year, edition, pages
AMER PHYSICAL SOC, 2019
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:kth:diva-243955 (URN)10.1103/PhysRevLett.122.020201 (DOI)000456041800001 ()30720322 (PubMedID)2-s2.0-85060652301 (Scopus ID)
Funder
Swedish Research Council, 2016-05167
Note

QC 20190304

Available from: 2019-03-04 Created: 2019-03-04 Last updated: 2019-06-26Bibliographically approved
Farrokh, A., Hallnas, M. & Langmann, E. (2019). Orthogonality of super‐Jack polynomials and a Hilbert space interpretation of deformed Calogero–Moser–Sutherland operators. Bulletin of the London Mathematical Society, 51(2), 353-370
Open this publication in new window or tab >>Orthogonality of super‐Jack polynomials and a Hilbert space interpretation of deformed Calogero–Moser–Sutherland operators
2019 (English)In: Bulletin of the London Mathematical Society, ISSN 0024-6093, E-ISSN 1469-2120, Vol. 51, no 2, p. 353-370Article in journal (Refereed) Published
Abstract [en]

We prove orthogonality and compute explicitly the (quadratic) norms for super-Jack polynomials SP lambda((z1, horizontal ellipsis ,zn),(w1, horizontal ellipsis ,wm);theta) with respect to a natural positive semi-definite, but degenerate, Hermitian product ⟨center dot,center dot⟩n,m,theta '. In case m=0 (or n=0), our product reduces to Macdonald's well-known inner product ⟨center dot,center dot⟩n,theta ', and we recover his corresponding orthogonality results for the Jack polynomials P lambda((z1, horizontal ellipsis ,zn);theta). From our main results, we readily infer that the kernel of ⟨center dot,center dot⟩n,m,theta ' is spanned by the super-Jack polynomials indexed by a partition lambda not containing the mxn rectangle (mn). As an application, we provide a Hilbert space interpretation of the deformed trigonometric Calogero-Moser-Sutherland operators of type A(n-1,m-1).

National Category
Natural Sciences
Research subject
Mathematics; Physics
Identifiers
urn:nbn:se:kth:diva-249098 (URN)10.1112/blms.12234 (DOI)000462907600013 ()
Funder
Swedish Research Council, 2016-05167Stiftelsen Olle Engkvist Byggmästare, 184-0573
Note

QC 20190424

Available from: 2019-04-10 Created: 2019-04-10 Last updated: 2019-04-24Bibliographically approved
Frank, R. L., Hainzl, C. & Langmann, E. (2019). The BCS critical temperature in a weak homogeneous magnetic field. Journal of Spectral Theory
Open this publication in new window or tab >>The BCS critical temperature in a weak homogeneous magnetic field
2019 (English)In: Journal of Spectral Theory, ISSN 1664-039X, E-ISSN 1664-0403Article in journal (Refereed) In press
Abstract [en]

We show that, within a linear approximation of BCS theory, a weak homogeneous magnetic field lowers the critical temperature by an explicit constant times the field strength, up to higher order terms. This provides a rigorous derivation and generalization of results obtained in the physics literature fromWHH theory of the upper critical magnetic field. A new ingredient in our proof is a rigorous phase approximation to control the effects of the magnetic field.

Keywords
Superconductivity, BCS theory, magnetic field
National Category
Natural Sciences
Research subject
Mathematics; Physics
Identifiers
urn:nbn:se:kth:diva-249107 (URN)10.4171/JST/270 (DOI)
Funder
Swedish Research Council, VR2016-05167Stiftelsen Olle Engkvist Byggmästare, 184-0573
Note

QC 20190521

Available from: 2019-04-10 Created: 2019-04-10 Last updated: 2019-05-21Bibliographically approved
Langmann, E., Triola, C. & Balatsky, A. V. (2019). Ubiquity of superconducting domes in Bardeen-Cooper-Schrieffer theory with finite-range potentials. Physical Review Letters
Open this publication in new window or tab >>Ubiquity of superconducting domes in Bardeen-Cooper-Schrieffer theory with finite-range potentials
2019 (English)In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114Article in journal (Refereed) In press
Abstract [en]

Based on recent progress in mathematical physics, we present a reliable method to analytically solve the linearized BCS gap equation for a large class of finite-range interaction potentials leading to s-wave superconductivity. With this analysis, we demonstrate that the monotonic growth of the superconducting critical temperature Tc with the carrier density, n, predicted by standard BCS theory, is an artifact of the simplifying assumption that the interaction is quasi-local. In contrast, we show that any well-defined non-local potential leads to a "superconducting dome", i.e. a non-monotonic Tc(n) exhibiting a maximum value at finite doping and going to zero for large n. This proves that, contrary to conventional wisdom, the presence of a superconducting dome is not necessarily an indication of competing orders, nor of exotic superconductivity. Our results provide a prototype example and guide towards improving ab-initio predictions of Tc for real materials.

National Category
Condensed Matter Physics
Research subject
Physics; Mathematics
Identifiers
urn:nbn:se:kth:diva-249115 (URN)000465182200011 ()2-s2.0-85064819657 (Scopus ID)
Funder
Swedish Research Council, 2016-05167
Note

QC 20190521

Available from: 2019-04-10 Created: 2019-04-10 Last updated: 2019-05-22Bibliographically approved
Langmann, E., Triola, C. & Balatsky, A. V. (2019). Ubiquity of Superconducting Domes in the Bardeen-Cooper-Schrieffer Theory with Finite-Range Potentials. Physical Review Letters, 122(15), Article ID 157001.
Open this publication in new window or tab >>Ubiquity of Superconducting Domes in the Bardeen-Cooper-Schrieffer Theory with Finite-Range Potentials
2019 (English)In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 122, no 15, article id 157001Article in journal (Refereed) Published
Abstract [en]

Based on recent progress in mathematical physics, we present a reliable method to analytically solve the linearized Bardeen-Cooper-Schrieffer (BCS) gap equation for a large class of finite-range interaction potentials leading to s-wave superconductivity. With this analysis, we demonstrate that the monotonic growth of the superconducting critical temperature Tc with the carrier density n predicted by standard BCS theory, is an artifact of the simplifying assumption that the interaction is quasilocal. In contrast, we show that any well-defined nonlocal potential leads to a "superconducting dome," i.e., a nonmonotonic Tc(n) exhibiting a maximum value at finite doping and going to zero for large n. This proves that, contrary to conventional wisdom, the presence of a superconducting dome is not necessarily an indication of competing orders, nor of exotic superconductivity.

Place, publisher, year, edition, pages
American Physical Society, 2019
Keywords
Shear waves, Bardeen-Cooper-Schrieffer, Bardeen-Cooper-Schrieffer theory, Interaction potentials, Mathematical physics, Monotonic growth, Nonlocal potentials, Simplifying assumptions, Superconducting critical temperatures, Domes
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:kth:diva-255910 (URN)10.1103/PhysRevLett.122.157001 (DOI)2-s2.0-85064819657 (Scopus ID)
Note

QC 20190822

Available from: 2019-08-22 Created: 2019-08-22 Last updated: 2019-08-22Bibliographically approved
Langmann, E. & Moosavi, P. (2018). Finite-Time Universality in Nonequilibrium CFT. Journal of statistical physics, 172(2), 353-378
Open this publication in new window or tab >>Finite-Time Universality in Nonequilibrium CFT
2018 (English)In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 172, no 2, p. 353-378Article in journal (Refereed) Published
Abstract [en]

Recently, remarkably simple exact results were presented about the dynamics of heat transport in the local Luttinger model for nonequilibrium initial states defined by position-dependent temperature profiles. We present mathematical details on how these results were obtained. We also give an alternative derivation using only algebraic relations involving the energy-momentum tensor which hold true in any unitary conformal field theory (CFT). This establishes a simple universal correspondence between initial temperature profiles and the resulting heat-wave propagation in CFT. We extend these results to larger classes of nonequilibrium states. It is proposed that such universal CFT relations provide benchmarks to identify nonuniversal properties of nonequilibrium dynamics in other models.

Place, publisher, year, edition, pages
Springer, 2018
Keywords
Nonequilibrium dynamics, Conformal field theory, Heat and charge transport, Luttinger model
National Category
Condensed Matter Physics
Identifiers
urn:nbn:se:kth:diva-232397 (URN)10.1007/s10955-018-2025-x (DOI)000437829200004 ()2-s2.0-85044457468 (Scopus ID)
Funder
Swedish Research Council, 2016-05167
Note

QC 20180726

Available from: 2018-07-26 Created: 2018-07-26 Last updated: 2019-05-20Bibliographically approved
Atai, F. & Langmann, E. (2018). Series Solutions of the Non-Stationary Heun Equation. SIGMA. Symmetry, Integrability and Geometry, 14, Article ID 011.
Open this publication in new window or tab >>Series Solutions of the Non-Stationary Heun Equation
2018 (English)In: SIGMA. Symmetry, Integrability and Geometry, ISSN 1815-0659, E-ISSN 1815-0659, Vol. 14, article id 011Article in journal (Refereed) Published
Abstract [en]

We consider the non-stationary Heun equation, also known as quantum Painleve VI, which has appeared in different works on quantum integrable models and conformal field theory. We use a generalized kernel function identity to transform the problem to solve this equation into a differential-difference equation which, as we show, can be solved by efficient recursive algorithms. We thus obtain series representations of solutions which provide elliptic generalizations of the Jacobi polynomials. These series reproduce, in a limiting case, a perturbative solution of the Heun equation due to Takemura, but our method is different in that we expand in non-conventional basis functions that allow us to obtain explicit formulas to all orders; in particular, for special parameter values, our series reduce to a single term.

Place, publisher, year, edition, pages
NATL ACAD SCI UKRAINE, INST MATH, 2018
Keywords
Heun equation, Lame equation, Kernel functions, quantum Painleve VI, perturbation theory
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-224070 (URN)10.3842/SIGMA.2018.011 (DOI)000425364200001 ()2-s2.0-85045072982 (Scopus ID)
Note

QC 20180314

Available from: 2018-03-14 Created: 2018-03-14 Last updated: 2018-03-14Bibliographically approved
Langmann, E., Lebowitz, J. L., Mastropietro, V. & Moosavi, P. (2017). Time evolution of the Luttinger model with nonuniform temperature profile. Physical Review B, 95(23), Article ID 235142.
Open this publication in new window or tab >>Time evolution of the Luttinger model with nonuniform temperature profile
2017 (English)In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 95, no 23, article id 235142Article in journal (Refereed) Published
Abstract [en]

We study the time evolution of a one-dimensional interacting fermion system described by the Luttinger model starting from a nonequilibrium state defined by a smooth temperature profile T (x). As a specific example we consider the case when T (x) is equal to T-L (T-R) far to the left (right). Using a series expansion in epsilon = 2(T-R -T-L)/(T-L + T-R), we compute the energy density, the heat current density, and the fermion two-point correlation function for all times t >= 0. For local (delta-function) interactions, the first two are computed to all orders, giving simple exact expressions involving the Schwarzian derivative of the integral of T (x). For nonlocal interactions, breaking scale invariance, we compute the nonequilibrium steady state (NESS) to all orders and the evolution to first order in epsilon. The heat current in the NESS is universal even when conformal invariance is broken by the interactions, and its dependence on T-L,T-R agrees with numerical results for the XXZ spin chain. Moreover, our analytical formulas predict peaks at short times in the transition region between different temperatures and show dispersion effects that, even if nonuniversal, are qualitatively similar to ones observed in numerical simulations for related models, such as spin chains and interacting lattice fermions.

Place, publisher, year, edition, pages
American Physical Society, 2017
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-211012 (URN)10.1103/PhysRevB.95.235142 (DOI)000404018700002 ()2-s2.0-85024365790 (Scopus ID)
Funder
Swedish Research Council, 2016-05167
Note

QC 20170712

Available from: 2017-07-12 Created: 2017-07-12 Last updated: 2018-11-20Bibliographically approved
Langmann, E. (2004). Exactly solvable models for 2D correlated fermions. Journal of Physics A: Mathematical and General, 37(2), 407-423
Open this publication in new window or tab >>Exactly solvable models for 2D correlated fermions
2004 (English)In: Journal of Physics A: Mathematical and General, Vol. 37, no 2, p. 407-423Article in journal (Refereed) Published
Abstract [en]

I discuss many-body models for correlated fermions in two space dimensions which can be solved exactly using group theory. The simplest example is a model of a quantum Hall system: two-dimensional (2D) fermions in a constant magnetic field and a particular non-local four-point interaction. It is exactly solvable due to a dynamical symmetry corresponding to the Lie algebra gl∞ ⊕ gl∞. There is an algorithm to construct all energy eigenvalues and eigenfunctions of this model. The latter are, in general, many-body states with spatial correlations. The model also has a non-trivial zero temperature phase diagram. I point out that this QH model can be obtained from a more realistic one using a truncation procedure generalizing a similar one leading to mean field theory. Applying this truncation procedure to other 2D fermion models I obtain various simplified models of increasing complexity which generalize mean field theory by taking into account non-trivial correlations but nevertheless are treatable by exact methods.

National Category
Condensed Matter Physics
Research subject
Physics; Mathematics
Identifiers
urn:nbn:se:kth:diva-249119 (URN)10.1088/0305-4470/37/2/010 (DOI)000188801800011 ()2-s2.0-0742288608 (Scopus ID)
Funder
Swedish Research Council
Note

QC 20190515

Available from: 2019-04-10 Created: 2019-04-10 Last updated: 2019-05-15Bibliographically approved
Langmann, E. (1999). Finding and solving Calogero-Moser type systems using Yang-Mills gauge theories. Nuclear Physics B, 563, 506-532
Open this publication in new window or tab >>Finding and solving Calogero-Moser type systems using Yang-Mills gauge theories
1999 (English)In: Nuclear Physics B, ISSN 0550-3213, E-ISSN 1873-1562, Vol. 563, p. 506-532Article in journal (Refereed) Published
National Category
Other Physics Topics
Research subject
Mathematics; Physics
Identifiers
urn:nbn:se:kth:diva-249135 (URN)10.1016/S0550-3213(99)00550-7 (DOI)
Note

QC 20190515

Available from: 2019-04-10 Created: 2019-04-10 Last updated: 2019-05-15Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0001-7481-2245

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