Investigations in the Bosonic Field Theory of Matrix Model

Abstract Entanglement or modular Hamiltonians play a crucial role in the investigation of correlations in quantum field theories. In particular, in 1 + 1 space–time dimensions, the spectra of entanglement Hamiltonians of conformal field theories (CFTs) for certain geometries are related to the spectra of the physical Hamiltonians of corresponding boundary CFTs. As a result, conformal invariance allows exact computation of the spectra of the entanglement Hamiltonians for these models. In this work, we perform this computation of the spectrum of the entanglement Hamiltonian for the free compactified boson CFT over a finite spatial interval. We compare the analytical results obtained for the continuum theory with numerical simulations of a lattice-regularized model for the CFT using density matrix renormalization group technique. To that end, we use a lattice regularization provided by superconducting quantum electronic circuits, built out of Josephson junctions and capacitors. Up to non-universal effects arising due to the lattice regularization, the numerical results are compatible with the predictions of the exact computations.Abstract Entanglement or modular Hamiltonians play a crucial role in the investigation of correlations in quantum field theories. In particular, in 1 + 1 space–time dimensions, the spectra of entanglement Hamiltonians of conformal field theories (CFTs) for certain geometries are related to the spectra of the physical Hamiltonians of corresponding boundary CFTs. As a result, conformal invariance allows exact computation of the spectra of the entanglement Hamiltonians for these models. In this work, we perform this computation of the spectrum of the entanglement Hamiltonian for the free compactified boson CFT over a finite spatial interval. We compare the analytical results obtained for the continuum theory with numerical simulations of a lattice-regularized model for the CFT using density matrix renormalization group technique. To that end, we use a lattice regularization provided by superconducting quantum electronic circuits, built out of Josephson junctions and capacitors. Up to non-universal effects arising due to the lattice regularization, the numerical results are compatible with the predictions of the exact computations.

arXiv:2004.14370Journal of Statistical Mechanics Theory and ExperimentAug 1, 202030 citations

Yangian-invariant field theory of matrix-vector models

Jean Avan, Antal Jevicki, J. Lee

arXiv:hep-th/9607083Nuclear Physics BFeb 1, 199714 citations

Renormalization in TT¯ -deformed nonintegrable theories

Subhroneel Chakrabarti, Arkajyoti Manna, Madhusudhan Raman

That the exact quantum S-matrix of $\mathrm{T}\overline{\mathrm{T}}$ -deformed field theories is known has interesting consequences for their perturbative renormalization. Recent investigations into the interplay between renormalization and integrable deformations have focused on those cases where the (undeformed) seed theories are integrable. In this paper, we study the perturbative renormalization of nonintegrable $\mathrm{T}\overline{\mathrm{T}}$ -deformed field theories, focusing on a theory of scalars with a quartic interaction. We show that in this theory, the 4-point 1-loop S-matrix exhibits features similar to its integrable cousins. We also carry out a similar analysis for the case of an integrable quantum field theory comprising a pair of chiral bosons. Our discussion of this latter theory supplies the first explicit example of a perturbative field theory computation in the formalism due to Sen.That the exact quantum S-matrix of $\mathrm{T}\overline{\mathrm{T}}$-deformed field theories is known has interesting consequences for their perturbative renormalization. Recent investigations into the interplay between renormalization and integrable deformations have focused on those cases where the (undeformed) seed theories are integrable. In this paper, we study the perturbative renormalization of nonintegrable $\mathrm{T}\overline{\mathrm{T}}$-deformed field theories, focusing on a theory of scalars with a quartic interaction. We show that in this theory, the 4-point 1-loop S-matrix exhibits features similar to its integrable cousins. We also carry out a similar analysis for the case of an integrable quantum field theory comprising a pair of chiral bosons. Our discussion of this latter theory supplies the first explicit example of a perturbative field theory computation in the formalism due to Sen.

arXiv:2204.03385Physical review. D/Physical review. D.May 24, 20228 citations

A slave‐boson mean‐field theory for general multi‐band Hubbard models

Jörg Bünemann

Abstract We introduce a new slave‐boson mean‐field theory which allows the investigation of general multi‐band Hubbard models. Unlike earlier attempts of such a generalization, in our approach the quantum‐mechanical problem is exactly reformulated in an extended Hilbert space of Fermions and Bosons before a mean‐field approximation is applied. Systems with superconducting order parameters are naturally included in our formalism. Our ground‐state energy functional agrees with the corresponding quantity derived within the Gutzwiller theory.Abstract We introduce a new slave‐boson mean‐field theory which allows the investigation of general multi‐band Hubbard models. Unlike earlier attempts of such a generalization, in our approach the quantum‐mechanical problem is exactly reformulated in an extended Hilbert space of Fermions and Bosons before a mean‐field approximation is applied. Systems with superconducting order parameters are naturally included in our formalism. Our ground‐state energy functional agrees with the corresponding quantity derived within the Gutzwiller theory.

arXiv:1002.3228physica status solidi (b)Jun 18, 20109 citations

That the exact quantum S-matrix of

\mathrm{T}\overline{\mathrm{T}}

-deformed field theories is known has interesting consequences for their perturbative renormalization. Recent investigations into the interplay between renormalization and integrable deformations have focused on those cases where the (undeformed) seed theories are integrable. In this paper, we study the perturbative renormalization of nonintegrable

\mathrm{T}\overline{\mathrm{T}}

-deformed field theories, focusing on a theory of scalars with a quartic interaction. We show that in this theory, the 4-point 1-loop S-matrix exhibits features similar to its integrable cousins. We also carry out a similar analysis for the case of an integrable quantum field theory comprising a pair of chiral bosons. Our discussion of this latter theory supplies the first explicit example of a perturbative field theory computation in the formalism due to Sen.