In this dissertation, the momentum-space entanglement properties of several quantum spin chains are investigated. In the second chapter we re- view important results on many-body entanglement. In the third chapter, we numerically study the momentum-space entanglement spectra of bosonic and fermionic formulations of the spin-1/2 XXZ chain [Phys. Rev. Lett. 113, 256404 (2014)]. We investigate the behavior of the entanglement gaps, present in both formulations, across quantum phase transitions in the XXZ chain. In both cases, finite size scaling suggests that the entanglement gap closure does not occur at the physical transition points. For bosons, we find that the entan- glement gap depends on the scaling dimension of the conformal field theory as varied by the X X Z anisotropy. For fermions, the infinite entanglement gap present at the XX point persists well past the phase transition at the Heisenberg point. We elaborate on how this may support the numerical study of phase transitions. In the third chapter, we advocate that in certain critical spin chains a gap in the momentum-space entanglement spectrum separates the universal part of the spectrum, which is determined by the associated conformal field theory, from the non-universal part, which is specific to the model [arXiv:1512.09030]. We provide affirmative evidence from multicritical spin-1 chains with low energy sectors described by the SU(2)2 or the SU(3)1 Wess-Zumino-Witten model. In chapter four, we study momentum- space en- tanglement in quantum spin-half ladders [Phys. Rev. B 93, 125107 (2016)]. When the system is gapped, we analytically find the momentum-space entan- glement Hamiltonian is described by a chiral conformal field theory with a central charge of two. When the system is gapless, the entanglement Hamil- tonian consists of one gapless mode that is linear in subsystem momentum and one mode with a flat dispersion relation. We also analytically include the effect of a certain irrelevant terms (in the renormalization group sense) on the entanglement spectrum. In chapter six, we investigate the momentum- space entanglement spectrum after a quantum quench [arXiv:1603.01997]. We show that the momentum-space entanglement spectrum of the XXZ spin- half chain possesses many universal features both in equilibrium and after a quantum quench.In this dissertation, the momentum-space entanglement properties of several quantum spin chains are investigated. In the second chapter we re- view important results on many-body entanglement. In the third chapter, we numerically study the momentum-space entanglement spectra of bosonic and fermionic formulations of the spin-1/2 XXZ chain [Phys. Rev. Lett. 113, 256404 (2014)]. We investigate the behavior of the entanglement gaps, present in both formulations, across quantum phase transitions in the XXZ chain. In both cases, finite size scaling suggests that the entanglement gap closure does not occur at the physical transition points. For bosons, we find that the entan- glement gap depends on the scaling dimension of the conformal field theory as varied by the X X Z anisotropy. For fermions, the infinite entanglement gap present at the XX point persists well past the phase transition at the Heisenberg point. We elaborate on how this may support the numerical study of phase transitions. In the third chapter, we advocate that in certain critical spin chains a gap in the momentum-space entanglement spectrum separates the universal part of the spectrum, which is determined by the associated conformal field theory, from the non-universal part, which is specific to the model [arXiv:1512.09030]. We provide affirmative evidence from multicritical spin-1 chains with low energy sectors described by the SU(2)2 or the SU(3)1 Wess-Zumino-Witten model. In chapter four, we study momentum- space en- tanglement in quantum spin-half ladders [Phys. Rev. B 93, 125107 (2016)]. When the system is gapped, we analytically find the momentum-space entan- glement Hamiltonian is described by a chiral conformal field theory with a central charge of two. When the system is gapless, the entanglement Hamil- tonian consists of one gapless mode that is linear in subsystem momentum and one mode with a flat dispersion relation. We also analytically include the effect of a certain irrelevant terms (in the renormalization group sense) on the entanglement spectrum. In chapter six, we investigate the momentum- space entanglement spectrum after a quantum quench [arXiv:1603.01997]. We show that the momentum-space entanglement spectrum of the XXZ spin- half chain possesses many universal features both in equilibrium and after a quantum quench.

Jan 1, 20160 citations

Entanglement in Spin Chains

K. Sengupta

arXiv:2109.02657Quantum science and technologyJan 1, 202232 citations

Momentum-space entanglement in Heisenberg spin-half ladders

Rex Lundgren

We study momentum-space entanglement in quantum spin-half ladders consisting of two coupled critical $XXZ$ spin-half chains, using field theoretical methods developed by Lundgren et al. [Phys. Rev. B 88, 245137 (2013)] and exact diagonalization. When the system is gapped, we analytically find that the momentum-space entanglement Hamiltonian is described by a chiral conformal field theory with a central charge of 2. This is in contrast to entanglement Hamiltonians of various real-space partitions of gapped-spin ladders that have a central charge of 1. When the system is gapless, the entanglement Hamiltonian consists of one gapless mode that is linear in subsystem momentum and one mode with a flat dispersion relation. In the gapless region, we extend the work of Lundgren et al. to include the effect of a certain irrelevant term on the entanglement spectrum. In both the gapless and gapped phases, the momentum-space entanglement entropy obeys a volume law. In the gapless region, we find a subleading constant term in the entanglement entropy which contains information about the underlying field theory of the system. The analytical predictions for the entanglement spectrum are consistent with results from exact diagonalization.We study momentum-space entanglement in quantum spin-half ladders consisting of two coupled critical $XXZ$ spin-half chains, using field theoretical methods developed by Lundgren et al. [Phys. Rev. B 88, 245137 (2013)] and exact diagonalization. When the system is gapped, we analytically find that the momentum-space entanglement Hamiltonian is described by a chiral conformal field theory with a central charge of 2. This is in contrast to entanglement Hamiltonians of various real-space partitions of gapped-spin ladders that have a central charge of 1. When the system is gapless, the entanglement Hamiltonian consists of one gapless mode that is linear in subsystem momentum and one mode with a flat dispersion relation. In the gapless region, we extend the work of Lundgren et al. to include the effect of a certain irrelevant term on the entanglement spectrum. In both the gapless and gapped phases, the momentum-space entanglement entropy obeys a volume law. In the gapless region, we find a subleading constant term in the entanglement entropy which contains information about the underlying field theory of the system. The analytical predictions for the entanglement spectrum are consistent with results from exact diagonalization.

arXiv:1412.8612Physical review. B./Physical review. BMar 2, 201612 citations

Entanglement Hamiltonians for quantum spin chains

Ronny Thomale, Stephan Rachel, Daniel P. Arovas +1 more

Bulletin of the American Physical SocietyMar 24, 20110 citations

Momentum-Space Entanglement Spectrum of Bosons and Fermions with Interactions

Rex Lundgren, Jonathan Blair, Martin Greiter +3 more

We study the momentum space entanglement spectra of bosonic and fermionic formulations of the spin-1/2 XXZ chain with analytical methods and exact diagonalization. We investigate the behavior of the entanglement gaps, present in both formulations, across quantum phase transitions in the XXZ chain. In both cases, finite size scaling suggests that the entanglement gap closure does not occur at the physical transition points. For bosons, we find that the entanglement gap observed in Thomale et al. [Phys. Rev. Lett. 105, 116805 (2010)] depends on the scaling dimension of the conformal field theory as varied by the XXZ anisotropy. For fermions, the infinite entanglement gap present at the XX point persists well past the phase transition at the Heisenberg point. We elaborate on how these shifted transition points in the entanglement spectra may support the numerical study of phase transitions in the momentum space density matrix renormalization group.We study the momentum space entanglement spectra of bosonic and fermionic formulations of the spin-1/2 XXZ chain with analytical methods and exact diagonalization. We investigate the behavior of the entanglement gaps, present in both formulations, across quantum phase transitions in the XXZ chain. In both cases, finite size scaling suggests that the entanglement gap closure does not occur at the physical transition points. For bosons, we find that the entanglement gap observed in Thomale et al. [Phys. Rev. Lett. 105, 116805 (2010)] depends on the scaling dimension of the conformal field theory as varied by the XXZ anisotropy. For fermions, the infinite entanglement gap present at the XX point persists well past the phase transition at the Heisenberg point. We elaborate on how these shifted transition points in the entanglement spectra may support the numerical study of phase transitions in the momentum space density matrix renormalization group.

arXiv:1404.7545Physical Review LettersDec 18, 201457 citations

We study momentum-space entanglement in quantum spin-half ladders consisting of two coupled critical

XXZ

spin-half chains, using field theoretical methods developed by Lundgren et al. [Phys. Rev. B 88, 245137 (2013)] and exact diagonalization. When the system is gapped, we analytically find that the momentum-space entanglement Hamiltonian is described by a chiral conformal field theory with a central charge of 2. This is in contrast to entanglement Hamiltonians of various real-space partitions of gapped-spin ladders that have a central charge of 1. When the system is gapless, the entanglement Hamiltonian consists of one gapless mode that is linear in subsystem momentum and one mode with a flat dispersion relation. In the gapless region, we extend the work of Lundgren et al. to include the effect of a certain irrelevant term on the entanglement spectrum. In both the gapless and gapped phases, the momentum-space entanglement entropy obeys a volume law. In the gapless region, we find a subleading constant term in the entanglement entropy which contains information about the underlying field theory of the system. The analytical predictions for the entanglement spectrum are consistent with results from exact diagonalization.