scholarly journals Thermal valence-bond-solid transition of quantum spins in two dimensions

2013 ◽  
Vol 87 (18) ◽  
Author(s):  
Songbo Jin ◽  
Anders W. Sandvik
Keyword(s):  
Valence Bond ◽  
Two Dimensions ◽  
Quantum Spins ◽  
Valence Bond Solid

Defected/decorated benzenoid/graphitic nanostructures

2008 ◽  
Vol 80 (7) ◽  
pp. 1399-1414 ◽  
Author(s):  
D. J. Klein
Keyword(s):  
Density Of States ◽  
Local Density ◽  
Valence Bond ◽  
Two Dimensions ◽  
Local Density Of States ◽  
Reliable Prediction ◽  
Vacancy Defects ◽  
Substitutional Defects ◽  
Local Defects ◽  
Property Characterization

Various decorations, functionalizations, or defects of conjugated benzenoid or graphitic networks are considered, with special attention to the case that the structures are possibly extended in one or two dimensions. This includes various polymers, their end structures, and defects of side groups or vacancies along the chain, strip, or nanotube. This approach further includes various boundary (or edge) structures on semi-infinite graphite, as well as various "quasi-local" defects in what is otherwise two-dimensionally infinite graphite, such defects encompassing vacancy defects, selected substitutional defects, and perhaps even dislocations and disclinations. There are many possible such nanostructures, but property characterization is ultimately desired. Attention is paid to consequent occurrences of defect-localized unpaired (or weakly paired) electrons, as formulated within a resonating valence bond (RVB) framework, especially as regards simple classically appealing theorems or rules. But a further molecular orbital (MO) view is developed. Note is made of associated modifications in the local density of states near the Fermi energy. Consonance of predictions from RVB and MO viewpoints is taken as an indicator of reliable prediction.

scholarly journals Supersymmetry and multicriticality in a ladder of constrained fermions

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Natalia Chepiga ◽  
Jiří Minář ◽  
Kareljan Schoutens
Keyword(s):  
Phase Diagram ◽  
Density Wave ◽  
Valence Bond ◽  
Lattice Models ◽  
Numerical Data ◽  
Universality Class ◽  
Density Profiles ◽  
Valence Bond Solid ◽  
Floating Phase ◽  
Solid Type

Supersymmetric lattice models of constrained fermions are known to feature exotic phenomena such as superfrustration, with an extensive degeneracy of ground states, the nature of which is however generally unknown. Here we address this issue by considering a superfrustrated model, which we deform from the supersymetric point. By numerically studying its two-parameter phase diagram, we reveal a rich phenomenology. The vicinity of the supersymmetric point features period-4 and period-5 density waves which are connected by a floating phase (incommensurate Luttinger liquid) with smoothly varying density. The supersymmetric point emerges as a multicritical point between these three phases. Inside the period-4 phase we report a valence-bond solid type ground state that persists up to the supersymmetric point. Our numerical data for transitions out of density-wave phases are consistent with the Pokrovsky-Talapov universality class. Furthermore, our analysis unveiled a period-3 phase with a boundary determined by a competition between single and two-particle instabilities accompanied by a doubling of the wavevector of the density profiles along a line in the phase diagram.

scholarly journals Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes

2021 ◽  
Author(s):  
Dongsheng Wang ◽  
Yunjiang Wang ◽  
Ningping Cao ◽  
Bei Zeng ◽  
Raymond Lafflamme
Keyword(s):  
Error Correction ◽  
Quantum Computation ◽  
Fault Tolerant ◽  
Valence Bond ◽  
Quantum Error Correction ◽  
Quantum Codes ◽  
Error Correction Codes ◽  
Exact Quantum ◽  
Valence Bond Solid ◽  
Quantum Error

Abstract In this work, we develop the theory of quasi-exact fault-tolerant quantum (QEQ) computation, which uses qubits encoded into quasi-exact quantum error-correction codes (``quasi codes''). By definition, a quasi code is a parametric approximate code that can become exact by tuning its parameters. The model of QEQ computation lies in between the two well-known ones: the usual noisy quantum computation without error correction and the usual fault-tolerant quantum computation, but closer to the later. Many notions of exact quantum codes need to be adjusted for the quasi setting. Here we develop quasi error-correction theory using quantum instrument, the notions of quasi universality, quasi code distances, and quasi thresholds, etc. We find a wide class of quasi codes which are called valence-bond-solid codes, and we use them as concrete examples to demonstrate QEQ computation.

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