scholarly journals Deformations of the boundary theory of the square-lattice AKLT model

2020 ◽  
Vol 102 (3) ◽  
Author(s):  
John Martyn ◽  
Kohtaro Kato ◽  
Angelo Lucia
Keyword(s):  
Square Lattice ◽  
Boundary Theory ◽  
Aklt Model

Influence of Flexible Side-Chains on the Breathing Phase Transition of Pillared Layer MOFs: A Force Field Investigation

2020 ◽  
Author(s):  
Julian Keupp ◽  
Johannes P. Dürholt ◽  
Rochus Schmid
Keyword(s):  
First Principles ◽  
Good Accuracy ◽  
Field Investigation ◽  
Square Lattice ◽  
Side Chain ◽  
Second Step ◽  
Side Chains ◽  
Dynamics Simulations ◽  
Complex Phenomena ◽  
Closed Pore

The prototypical pillared layer MOFs, formed by a square lattice of paddle-<br>wheel units and connected by dinitrogen pillars, can undergo a breathing phase<br>transition by a “wine-rack” type motion of the square lattice. We studied this not<br>yet fully understood behavior using an accurate first principles parameterized force<br>field (MOF-FF) for larger nanocrystallites on the example of Zn 2 (bdc) 2 (dabco) [bdc:<br>benzenedicarboxylate, dabco: (1,4-diazabicyclo[2.2.2]octane)] and found clear indi-<br>cations for an interface between a closed and an open pore phase traveling through<br>the system during the phase transformation [Adv. Theory Simul. 2019, 2, 11]. In<br>conventional simulations in small supercells this mechanism is prevented by periodic<br>boundary conditions (PBC), enforcing a synchronous transformation of the entire<br>crystal. Here, we extend this investigation to pillared layer MOFs with flexible<br>side-chains, attached to the linker. Such functionalized (fu-)MOFs are experimen-<br>tally known to have different properties with the side-chains acting as fixed guest<br>molecules. First, in order to extend the parameterization for such flexible groups,<br>1a new parametrization strategy for MOF-FF had to be developed, using a multi-<br>structure force based fit method. The resulting parametrization for a library of<br>fu-MOFs is then validated with respect to a set of reference systems and shows very<br>good accuracy. In the second step, a series of fu-MOFs with increasing side-chain<br>length is studied with respect to the influence of the side-chains on the breathing<br>behavior. For small supercells in PBC a systematic trend of the closed pore volume<br>with the chain length is observed. However, for a nanocrystallite model a distinct<br>interface between a closed and an open pore phase is visible only for the short chain<br>length, whereas for longer chains the interface broadens and a nearly concerted trans-<br>formation is observed. Only by molecular dynamics simulations using accurate force<br>fields such complex phenomena can be studied on a molecular level.

A STUDY OF GEOMETRICALLY STABLE PATTERNS ON A SQUARE LATTICE ECONOMY

2018 ◽  
Vol 74 (4) ◽  
pp. 411-425
Author(s):  
Yosuke KOGURE ◽  
Mikihisa ONDA ◽  
Minoru OSAWA ◽  
Yuki TAKAYAMA ◽  
Kiyohiro IKEDA
Keyword(s):  
Square Lattice

scholarly journals Universal Qudit Hamiltonians

2021 ◽  
Author(s):  
Stephen Piddock ◽  
Ashley Montanaro
Keyword(s):  
State Energy ◽  
Entangled State ◽  
Quantum Computers ◽  
List Type ◽  
Universal Family ◽  
Finite Dimensional ◽  
Universal Quantum ◽  
Aklt Model ◽  
Almost All ◽  
Natural Way

AbstractA family of quantum Hamiltonians is said to be universal if any other finite-dimensional Hamiltonian can be approximately encoded within the low-energy space of a Hamiltonian from that family. If the encoding is efficient, universal families of Hamiltonians can be used as universal analogue quantum simulators and universal quantum computers, and the problem of approximately determining the ground-state energy of a Hamiltonian from a universal family is QMA-complete. One natural way to categorise Hamiltonians into families is in terms of the interactions they are built from. Here we prove universality of some important classes of interactions on qudits (d-level systems): We completely characterise the k-qudit interactions which are universal, if augmented with arbitrary Hermitian 1-local terms. We find that, for all $$k \geqslant 2$$ k ⩾ 2 and all local dimensions $$d \geqslant 2$$ d ⩾ 2 , almost all such interactions are universal aside from a simple stoquastic class. We prove universality of generalisations of the Heisenberg model that are ubiquitous in condensed-matter physics, even if free 1-local terms are not provided. We show that the SU(d) and SU(2) Heisenberg interactions are universal for all local dimensions $$d \geqslant 2$$ d ⩾ 2 (spin $$\geqslant 1/2$$ ⩾ 1 / 2 ), implying that a quantum variant of the Max-d-Cut problem is QMA-complete. We also show that for $$d=3$$ d = 3 all bilinear-biquadratic Heisenberg interactions are universal. One example is the general AKLT model. We prove universality of any interaction proportional to the projector onto a pure entangled state.

scholarly journals Publisher Correction: Enhanced thermal Hall effect in the square-lattice Néel state

2021 ◽  
Author(s):  
Rhine Samajdar ◽  
Mathias S. Scheurer ◽  
Shubhayu Chatterjee ◽  
Haoyu Guo ◽  
Cenke Xu ◽  
...  
Keyword(s):  
Hall Effect ◽  
Square Lattice

Proposal for dispersion compensating square-lattice photonic crystal fiber

2021 ◽  
Vol 17 (3) ◽  
pp. 160-164
Author(s):  
Ashraful Hossain Howlader ◽  
Md. Sherajul Islam ◽  
S. M. A. Razzak
Keyword(s):  
Photonic Crystal ◽  
Photonic Crystal Fiber ◽  
Square Lattice ◽  
Crystal Fiber

Double-core photonic crystal fiber with square lattice

2004 ◽  
Author(s):  
Ryszard Buczynski ◽  
Przemyslaw Szarniak ◽  
Dariusz Pysz ◽  
Ireneusz Kujawa ◽  
Ryszard Stepien ◽  
...  
Keyword(s):  
Photonic Crystal ◽  
Photonic Crystal Fiber ◽  
Square Lattice ◽  
Crystal Fiber

Two‐Dimensional V‐VI Binary Nanosheets with Square Lattice: A Theoretical Investigation

2021 ◽  
Author(s):  
Xin Qiao ◽  
Xiaodong Lv ◽  
Yinan Dong ◽  
Yanping Yang ◽  
Fengyu Li
Keyword(s):  
Theoretical Investigation ◽  
Square Lattice ◽  
Two Dimensional
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