scholarly journals Energy transport in Z3 chiral clock model

2021 ◽  
Author(s):  
NAVEEN NISHAD ◽  
GJ Sreejith
Keyword(s):  
Energy Transport ◽  
Ballistic Transport ◽  
Finite Size ◽  
Transverse Field ◽  
Spin Coupling ◽  
Scaling Exponent ◽  
Matrix Product ◽  
Clock Model ◽  
Chirality Parameter ◽  
Transverse Field Ising Model

Abstract We characterize the energy transport in a one dimensional Z3 chiral clock model. The model generalizes the Z2 symmetric transverse field Ising model (TFIM). The model is parametrized by a chirality parameter Θ, in addition to f and J which are analogous to the transverse field and the nearest neighbour spin coupling in the TFIM. Unlike the well studied TFIM and XYZ models, does not transform to a fermionic system. We use a matrix product states implementation of the Lindblad master equation to obtain the non-equilibrium steady state (NESS) in systems of sizes up to 48. We present the estimated NESS current and its scaling exponent γ as a function of Θ at different f/J. The estimated γ(f/J,Θ) point to a ballistic energy transport along a line of integrable points f=Jcos{3Θ} in the parameter space; all other points deviate from ballistic transport. Analysis of finite size effects within the available system sizes suggest a diffusive behavior away from the integrable points.

scholarly journals Quantum transverse-field Ising model on an infinite tree from matrix product states

2008 ◽  
Vol 77 (21) ◽  
Author(s):  
Daniel Nagaj ◽  
Edward Farhi ◽  
Jeffrey Goldstone ◽  
Peter Shor ◽  
Igor Sylvester
Keyword(s):  
Ising Model ◽  
Transverse Field ◽  
Matrix Product ◽  
Matrix Product States ◽  
Infinite Tree ◽  
Transverse Field Ising Model

scholarly journals Localisation determines the optimal noise rate for quantum transport

2021 ◽  
Author(s):  
Alexandre Coates ◽  
Brendon W Lovett ◽  
Erik Gauger
Keyword(s):  
Energy Transport ◽  
Optimal Transport ◽  
Detailed Balance ◽  
Finite Size ◽  
Temperature Limit ◽  
Transport Efficiency ◽  
Size Dependent ◽  
Noise Rate ◽  
Pure Dephasing ◽  
The Impact

Abstract Environmental noise plays a key role in determining the efficiency of transport in quantum systems. However, disorder and localisation alter the impact of such noise on energy transport. To provide a deeper understanding of this relationship we perform a systematic study of the connection between eigenstate localisation and the optimal dephasing rate in 1D chains. The effects of energy gradients and disorder on chains of various lengths are evaluated and we demonstrate how optimal transport efficiency is determined by both size-independent, as well as size-dependent factors. By discussing how size-dependent influences emerge from finite size effects we establish when these effects are suppressed, and show that a simple power law captures the interplay between size-dependent and size-independent responses. Moving beyond phenomenological pure dephasing, we implement a finite temperature Bloch-Redfield model that captures detailed balance. We show that the relationship between localisation and optimal environmental coupling strength continues to apply at intermediate and high temperature but breaks down in the low temperature limit.

scholarly journals Correlation functions for a strongly coupled boson system and plane partitions

2011 ◽  
Vol 369 (1939) ◽  
pp. 1319-1333 ◽  
Author(s):  
Nikolay Bogoliubov ◽  
Jussi Timonen
Keyword(s):  
Correlation Functions ◽  
Finite Size ◽  
Temperature Limit ◽  
Phase Model ◽  
Strong Interactions ◽  
Scaling Exponent ◽  
Strongly Correlated ◽  
Strongly Coupled ◽  
Plane Partitions ◽  
Hopping Model

A quantum phase model is introduced as a limit for very strong interactions of a strongly correlated q -boson hopping model. The exact solution of the phase model is reviewed, and solutions are also provided for two correlation functions of the model. Explicit expressions, including both amplitude and scaling exponent, are derived for these correlation functions in the low temperature limit. The amplitudes were found to be related to the number of plane partitions contained in boxes of finite size.

scholarly journals Pseudo-Yang-Lee Edge Singularity Critical Behavior in a Non-Hermitian Ising Model

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 780
Author(s):  
Liang-Jun Zhai ◽  
Guang-Yao Huang ◽  
Huai-Yu Wang
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Critical Behavior ◽  
Critical Region ◽  
Numerical Study ◽  
Transverse Field ◽  
Scaling Theory ◽  
New Order ◽  
Edge Singularity ◽  
Transverse Field Ising Model

The quantum phase transition of a one-dimensional transverse field Ising model in an imaginary longitudinal field is studied. A new order parameter M is introduced to describe the critical behaviors in the Yang-Lee edge singularity (YLES). The M does not diverge at the YLES point, a behavior different from other usual parameters. We term this unusual critical behavior around YLES as the pseudo-YLES. To investigate the static and driven dynamics of M, the (1+1) dimensional ferromagnetic-paramagnetic phase transition ((1+1) D FPPT) critical region, (0+1) D YLES critical region and the (1+1) D YLES critical region of the model are selected. Our numerical study shows that the (1+1) D FPPT scaling theory, the (0+1) D YLES scaling theory and (1+1) D YLES scaling theory are applicable to describe the critical behaviors of M, demonstrating that M could be a good indicator to detect the phase transition around YLES. Since M has finite value around YLES, it is expected that M could be quantitatively measured in experiments.

scholarly journals Optimizing a quantum reservoir computer for time series prediction

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Aki Kutvonen ◽  
Keisuke Fujii ◽  
Takahiro Sagawa
Keyword(s):  
Time Series ◽  
Language Processing ◽  
Quantum Dynamics ◽  
Time Series Prediction ◽  
Transverse Field ◽  
Memory Capacity ◽  
Great Promise ◽  
Real World Data ◽  
Spin Interactions ◽  
Transverse Field Ising Model

Abstract Quantum computing and neural networks show great promise for the future of information processing. In this paper we study a quantum reservoir computer (QRC), a framework harnessing quantum dynamics and designed for fast and efficient solving of temporal machine learning tasks such as speech recognition, time series prediction and natural language processing. Specifically, we study memory capacity and accuracy of a quantum reservoir computer based on the fully connected transverse field Ising model by investigating different forms of inter-spin interactions and computing timescales. We show that variation in inter-spin interactions leads to a better memory capacity in general, by engineering the type of interactions the capacity can be greatly enhanced and there exists an optimal timescale at which the capacity is maximized. To connect computational capabilities to physical properties of the underlaying system, we also study the out-of-time-ordered correlator and find that its faster decay implies a more accurate memory. Furthermore, as an example application on real world data, we use QRC to predict stock values.

scholarly journals Worm-algorithm-type simulation of the quantum transverse-field Ising model

2020 ◽  
Vol 102 (9) ◽  
Author(s):  
Chun-Jiong Huang ◽  
Longxiang Liu ◽  
Yi Jiang ◽  
Youjin Deng
Keyword(s):  
Ising Model ◽  
Transverse Field ◽  
Transverse Field Ising Model
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