Abstract
In recent years, the infinite time-evolution block decimation (iTEBD) method has been demonstrated to be one of the most efficient and powerful numerical schemes for time-evolution in one-dimensional quantum many-body systems. However, a major shortcoming of the method, along with other state-of-the-art algorithms for many-body dynamics, has been their restriction to one spatial dimension. We present an algorithm based on a \textit{hybrid} extension of iTEBD where finite blocks of a chain are first locally time-evolved before an iTEBD-like method combines these processes globally. This in turn permits simulating the dynamics of many-body systems in the thermodynamic limit in $d\geq1$ dimensions including in the presence of long-range interactions. Our work paves the way for simulating the dynamics of many-body phenomena that occur exclusively in higher dimensions, and whose numerical treatments have hitherto been limited to exact diagonalization of small systems, which fundamentally limits a proper investigation of dynamical criticality. We expect the algorithm presented here to be of significant importance to validating and guiding investigations in state-of-the-art ion-trap and ultracold-atom experiments.
Highlights
Over the past century, a lot of research in condensed matter physics has focused on exploring, understanding, and engineering exotic phenomena emerging from the interactions of many particles whose individual behavior falls short of the richness contained in that of their collective gestalt [1]
This in turn permits simulating the dynamics of many-body systems in spatial dimensions d 1 where the thermodynamic limit is achieved along one spatial dimension and where long-range interactions can be included
Our work paves the way for simulating the dynamics of many-body phenomena that occur exclusively in higher dimensions and whose numerical treatments have hitherto been limited to exact diagonalization of small systems, which fundamentally limits a proper investigation of dynamical criticality
Summary
A lot of research in condensed matter physics has focused on exploring, understanding, and engineering exotic phenomena emerging from the interactions of many particles whose individual behavior falls short of the richness contained in that of their collective gestalt [1]. Numerical studies on both of the above concepts of dynamical phase transitions have been restricted to one-dimensional (1D) many-body Hamiltonians, with the exception of integrable models, such mean-field and exactly solvable free-fermionic systems, and small finite twodimensional lattices studied in exact diagonalization where ascertaining dynamical critical behavior is necessarily inadequate so far away from the thermodynamic limit. We introduce a new MPS algorithm that can simulate the dynamics of effectively two-dimensional (2D) systems by time-evolving mappings thereof to 1D chains with long-range fixed-length interaction profiles. This method is a combination of two techniques.
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