Elliott Hershel Lieb - Selected publications#

E.H. Lieb, F.Y. Wu, Absence of Mott transition in an exact solution of short-range 1-band model in 1 dimension, Phys. Rev. Lett. 20, 1445 (1968); 2077 WoS citations

E.H. Lieb, T. Schultz, D. Mattis, 2 soluble models of an antiferromagnetic chain, Ann. Phys. 16, 407 (1961); 1883 WoS citations

E.H. Lieb, W. Liniger, Exact analysis of an interacting Bose gas. 1. general solution and the ground state, Phys. Rev. 130, 1605 (1963); 1243 WoS citations

E.H.Lieb and W. Liniger, Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum, Phys. Rev. 130, 1616-1624 (1963).

I. Affleck, T. Kennedy, E.H. Lieb, H. Tasaki, Rigorous results on valence-bod ground-states in antiferromagnets, Phys. Rev. Lett. 59, 799 (1987); 961 WoS citations

I. Affleck, T. Kennedy, E.H. Lieb, H. Tasaki, Valence bond ground-states in isotropic quantum antiferromagnets, Commun. Math. Phys. 115, 477 (1988); 797 WoS citations

T.D. Schultz, D.C. Mattis and E.H.Lieb, Two-Dimensional Ising Model as a Soluble Problem of Many Fermions, Rev. Mod. Phys. 36, 856-871 (1964).

E.H.Lieb, Exact Solution of the Problem of the Entropy of Two-Dimensional Ice, Phys. Rev. Lett. 18, 692-694 (1967).

E.H.Lieb, Exact Solution of the $F$ Model of an Antiferroelectric, Phys. Rev. Lett. 18, 1046-1048 (1967).

E.H.Lieb, Exact Solution of the Two-Dimensional Slater KDP Model of a Ferroelectric, Phys. Rev. Lett. 19, 108-110 (1967).

\item{\c32.} E.H.Lieb, Residual Entropy of Square Ice, Phys. Rev. 162, 162-172 (1967).

E.H.Lieb and J.L. Lebowitz, Existence of Thermodynamics for Real Matter with Coulomb Forces, Phys. Rev. Lett. 22, 631-634 (1969).

H. Araki and E.H. Lieb Entropy Inequalities, Commun. Math. Phys. 18, 160-170 (1970).

O.J. Heilmann and E.H. Lieb, Monomers and Dimers, Phys. Rev. Lett. 24, 1412-1414 (1970).

H.N.V. Temperley and E.H. Lieb, Relations between the 'Percolation' and 'Colouring' Problem and Other Graph-Theoretical Problems Associated with Regular Planar Lattices: Some Exact Results for the `Percolation' Problem, Proc. Roy. Soc. A322, 251-280 (1971).

J.L. Lebowitz and E.H. Lieb, The Constitution of Matter: Existence of Thermodynamics for Systems Composed of Electrons and Nuclei, Adv. in Math. 9, 316-398 (1972).

O.J. Heilmann and E.H. Lieb, Theory of Monomer-Dimer Systems, Commun. Math. Phys. 25, 190-232 (1972). Errata 27, 166 (1972).

E.H. Lieb and D.W. Robinson, The Finite Group Velocity of Quantum Spin Systems, Commun. Math. Phys. 28, 251-257 (1972).

E.H. Lieb, Convex Trace Functions and the Wigner-Yanase-Dyson Conjecture, Adv. in Math. 11, 267-288 (1973).

E.H. Lieb and M.B. Ruskai, A Fundamental Property of Quantum Mechanical Entropy, Phys. Rev. Lett. 30, 434-436 (1973).

E.H. Lieb and M.B. Ruskai, Proof of the Strong Subadditivity of Quantum-Mechanical Entropy, J. Math. Phys. 14, 1938-1941 (1973).

K. Hepp and E.H. Lieb, On the Superradiant Phase Transition for Molecules in a Quantized Radiation Field: The Dicke Maser Model, Annals of Phys. (N.Y.) 76, 360-404 (1973).

E.H. Lieb, The Classical Limit of Quantum Spin Systems, Commun. Math. Phys. {\bf 31}, 327-340 (1973).

E.H. Lieb and B. Simon, Thomas-Fermi Theory Revisited, Phys. Rev. Lett. 31, 681-683 (1973).

E.H. Lieb and B. Simon, On Solutions to the Hartree-Fock Problem for Atoms and Molecules, J. Chem. Physics 61, 735-736 (1974).

E.H. Lieb and W. Thirring, Bound for the Kinetic Energy of Fermions which Proves the Stability of Matter, Phys. Rev. Lett. 35, 687-689 (1975). Errata {\bf 35}, 1116 (1975).

H.J. Brascamp and E.H. Lieb, Some Inequalities for Gaussian Measures and the Long-Range Order of the One-Dimensional Plasma, lecture at Conference on Functional Integration, Cumberland Lodge, England. Functional Integration and its Applications, A.M. Arthurs ed., Clarendon Press, 1-14 (1975).

E.H. Lieb and W. Thirring, Inequalities for the Moments of the Eigenvalues of the Schrödinger Hamiltonian and Their Relation to Sobolev Inequalities, in Studies in Mathematical Physics, E. Lieb, B. Simon, A. Wightman eds., Princeton University Press, 269-303 (1976).

E.H. Lieb and B. Simon, Thomas-Fermi Theory of Atoms, Molecules and Solids, Adv. in Math. 23, 22-116 (1977).

E.H. Lieb and B. Simon, The Hartree-Fock Theory for Coulomb Systems, Commun. Math. Phys. 53, 185-194 (1977).

F.J. Dyson, E.H. Lieb and B. Simon) Phase Transitions in Quantum Spin
Systems with Isotropic and Non-Isotropic Interactions, J. Stat. Phys.
18, 335-383 (1978).

J. Fr\"ohlich, R. Israel, E.H. Lieb and B. Simon, PhaseTransitions and Reflection Positivity. I. General Theory and Long Range Lattice Models, Commun. Math. Phys. 62, 1-34 (1978).

E.H Lieb, Variational Principle for Many-Fermion Systems, Phys. Rev. Lett. 46, 457-459 (1981). Errata 47, 69 (1981).

E.H. Lieb, Sharp Constants in the Hardy-Littlewood-Sobolev and Related Inequalities, Annals of Math. 118, 349-374 (1983).

E.H. Lieb, Density Functionals for Coulomb Systems, Int. Jour. Quant. Chem. 24, 243-277 (1983).

E.H. Lieb, Flux Phase of the Half-Filled Band, Phys. Rev. Lett. 73, 2158-2161 (1994).

E.H. Lieb and J. Yngvason, The Physics and Mathematics of the Second Law of Thermodynamics, Physics Reports 310, 1-96 (1999).

E.H. Lieb and J. Yngvason, Ground State Energy of the Low Density Bose Gas, Phys. Rev. Lett. 80, 2504-2507 (1998).

E. Carlen and E.H. Lieb, A Minkowski Type Trace Inequality and Strong Subadditivity of Quantum Entropy II: Convexity and Concavity, Lett. Math. Phys. 83, 107-126 (2008)

E.H. Lieb and R. Seiringer, Proof of Bose-Einstein Condensation for Dilute Trapped Gases, Phys. Rev. Lett. 88, \#170409--1-4 (2002).

E.H. Lieb and R. Seiringer, Derivation of the Gross-Pitaevskii Equation for Rotating Bose Gases, Commun. Math. Phys. 264, 505-537 (2006).


R.L. Frank, E.H. Lieb, R. Seiringer, Hardy-Lieb-Thirring Inequalities for fractional Schroedinger operators, J. Amer. Math. Soc. 21, 925 (2008)

R.L. Frank, E.H. Lieb, Sharp constants in several inequalities on the Heisenberg group, Ann. Math. 176, 349 (2012)

A. Giuliani, E.H. Lieb, R. Seiringer, Realization of stripes and slabs in two and three dimensions, Phys. Rev. B 88, 064401 (2013)

R. Frank, M. Lewin and R. Seiringer, Strichartz Inequality for Orthonormal Functions, Jour. European Math. Soc., (in press)

R.L. Frank. M. Lewin, E.H. Lieb, R. Seiringer, Energy cost to make a hole in the Fermi Sea, Phys. Rev. Lett. 106, 150402 (2011)

E.H. Lieb, R. Seiringer, The stability of matter in quantum mechanics, Cambridge Univ. Press (2010)