Product vacua with boundary states

Bachmann, Sven; Nachtergaele, Bruno

doi:10.1103/physrevb.86.035149

Cited by 18 publications

(34 citation statements)

References 33 publications

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“…The goal of this work is to determine for each combination of unit inward pointing normal m ∈ R d and parameters λ ∈ (0, ∞) d whether the gap γ(H D ) vanishes or not and to find explicit bounds for the gap whenever possible. The case d = 1 was treated in [1] where it was shown that model is gapless if λ = 1 and gapped otherwise. Special for the case d = 1 is that the ground state space for the half-infinite chain [1, ∞) ⊂ Z is two-dimensional if m log λ < 0 and one-dimensional if m log λ ≥ 0.…”

Section: Definition Of the Model And Main Resultsmentioning

confidence: 99%

Spectral Gap and Edge Excitations of d-Dimensional PVBS Models on Half-Spaces

2016

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We analyze a class of quantum spin models defined on half-spaces in the d-dimensional hypercubic lattice bounded by a hyperplane with inward unit normal vector m ∈ R d . The family of models was previously introduced as the single species Product Vacua with Boundary States (PVBS) model, which is a spin-1/2 model with a XXZ-type nearest neighbor interactions depending on parameters λ j ∈ (0, ∞), one for each coordinate direction. For any given values of the parameters, we prove an upper bound for the spectral gap above the unique ground state of these models, which vanishes for exactly one direction of the normal vector m. For all other choices of m we derive a positive lower bound of the spectral gap, except for the case λ 1 = · · · = λ d = 1, which is known to have gapless excitations in the bulk.

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Section: Definition Of the Model And Main Resultsmentioning

confidence: 99%

Spectral Gap and Edge Excitations of d-Dimensional PVBS Models on Half-Spaces

2016

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“…Bacterial Strains, Phages, and Culture Conditions-Genetic experiments were carried out in E. coli strain SG20781 (32), MC4100 (33), W3110, or MG1655 (34). The deletion/replacement of the lon gene by a Kan R cassette was carried out as described (35) using pKD4 as the DNA template (36).…”

Section: Methodsmentioning

confidence: 99%

Lon Protease Quality Control of Presecretory Proteins in Escherichia coli and Its Dependence on the SecB and DnaJ (Hsp40) Chaperones

Sakr

Cirinesi

Ullers³

et al. 2010

Journal of Biological Chemistry

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Various environmental insults result in irreversible damage to proteins and protein complexes. To cope, cells have evolved dedicated protein quality control mechanisms involving molecular chaperones and proteases. Here, we provide both genetic and biochemical evidence that the Lon protease and the SecB and DnaJ/Hsp40 chaperones are involved in the quality control of presecretory proteins in Escherichia coli. We showed that mutations in the lon gene alleviate the cold-sensitive phenotype of a secB mutant. Such suppression was not observed with either clpP or clpQ protease mutants. In comparison to the respective single mutants, the double secB lon mutant strongly accumulates aggregates of SecB substrates at physiological temperatures, suggesting that the chaperone and the protease share substrates. These observations were extended in vitro by showing that the main substrates identified in secB lon aggregates, namely proOmpF and proOmpC, are highly sensitive to specific degradation by Lon. In contrast, both substrates are significantly protected from Lon degradation by SecB. Interestingly, the chaperone DnaJ by itself protects substrates better from Lon degradation than SecB or the complete DnaK/DnaJ/GrpE chaperone machinery. In agreement with this finding, a DnaJ mutant protein that does not functionally interact in vivo with DnaK efficiently suppresses the SecB cold-sensitive phenotype, highlighting the role of DnaJ in assisting presecretory proteins. Taken together, our data suggest that when the Sec secretion pathway is compromised, a pool of presecretory proteins is transiently maintained in a translocation-competent state and, thus, protected from Lon degradation by either the SecB or DnaJ chaperones.Molecular chaperones comprise a large group of highly conserved proteins that aid protein folding, transit across biological membranes, and quality control as well as assembly and disassembly of protein complexes (1-3). Molecular chaperones act by repeated binding and release of aggregation-sensitive polypeptide segments normally found buried in the final folded structure of a substrate. Although predominantly found during de novo protein synthesis or after a denaturing stress leading to protein misfolding or aggregation, such aggregation-prone segments can also be transiently exposed in native multiprotein complexes. In this case molecular chaperone binding coordinates subtle conformational changes affecting biological functions (4, 5).In the bacterium Escherichia coli, intracellular protein folding is mainly orchestrated by the chaperones Trigger Factor (TF), 2 DnaK/Hsp70, and GroEL/Hsp60. The chaperone TF binds near the ribosomal polypeptide exit with a 1:1 stoichiometry, forming a protective "cradle" for emerging nascent chains. Because of its advantageous localization, TF may interact cotranslationally with most nascent polypeptides (6, 7). TF cycles on and off the ribosome, and both ribosome-bound or released polypeptide chains can stay post-translationally bound to ribosome-free TF for a prolonged period ...

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“…This is precisely the same structure occurring in, e.g., product vacua with boundary states [31,32] , so simplifying P E also yields insight into the structure of RG fixed points. not have any fixed points.…”

Section: Adding Decaymentioning

confidence: 84%

Asymptotics of quantum channels: conserved quantities, an adiabatic limit, and matrix product states

Albert

2019

Quantum

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This work derives an analytical formula for the asymptotic state-the quantum state resulting from an infinite number of applications of a general quantum channel on some initial state. For channels admitting multiple fixed or rotating points, conserved quantities-the left fixed/rotating points of the channeldetermine the dependence of the asymptotic state on the initial state. The formula stems from a Noether-like theorem stating that, for any channel admitting a full-rank fixed point, conserved quantities commute with that channel's Kraus operators up to a phase. The formula is applied to adiabatic transport of the fixed-point space of channels, revealing cases where the dissipative/spectral gap can close during any segment of the adiabatic path. The formula is also applied to calculate expectation values of noninjective matrix product states (MPS) in the thermodynamic limit, revealing that those expectation values can also be calculated using an MPS with reduced bond dimension and a modified boundary.

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Product vacua with boundary states

Cited by 18 publications

References 33 publications

Spectral Gap and Edge Excitations of d-Dimensional PVBS Models on Half-Spaces

Spectral Gap and Edge Excitations of d-Dimensional PVBS Models on Half-Spaces

Lon Protease Quality Control of Presecretory Proteins in Escherichia coli and Its Dependence on the SecB and DnaJ (Hsp40) Chaperones

Asymptotics of quantum channels: conserved quantities, an adiabatic limit, and matrix product states

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