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We establish an important duality correspondence between topological order in quantum many body systems and criticality in ferromagnetic classical spin systems. We show how such a correspondence leads to a classical and simple procedure for…
Quantum computers promise a highly efficient approach to investigate quantum phase transitions, which describe abrupt changes between different ground states of many-body systems. At quantum critical points, the divergent correlation length…
Quantum critical points in quasiperiodic magnets can realize new universality classes, with critical properties distinct from those of clean or disordered systems. Here, we study quantum phase transitions separating ferromagnetic and…
The disorder-driven phase transition of the RFIM is observed using exact ground-state computer simulations for hyper cubic lattices in d=5,6,7 dimensions. Finite-size scaling analyses are used to calculate the critical point and the…
It is by now well-known that ground states of gapped one-dimensional (1d) quantum-many body systems with short-range interactions can be studied efficiently using classical computers and matrix product state techniques. A corresponding…
Noninvertible symmetry generalizes traditional group symmetries, advancing our understanding of quantum matter, especially one-dimensional gapped quantum systems. In critical lattice models, it is usually realized as emergent symmetries in…
A generalization of matrix product states (MPS) is introduced which is suitable for describing interacting quantum systems in two and three dimensions. These scale-renormalized matrix-product states (SR-MPS) are based on a course-graining…
Common wisdom says that the entanglement of fermionic systems can be low in the second quantization formalism but is extremely large in the first quantization. Hence Matrix Product State (MPS) methods based on moderate entanglement have…
In quantum physics, multiparticle systems are described by quantum states acting on tensor products of Hilbert spaces. This product structure leads to the distinction between product states and entangled states; moreover, one can quantify…
Temperature estimation of interacting quantum many-body systems is both a challenging task and topic of interest in quantum metrology, given that critical behavior at phase transitions can boost the metrological sensitivity. Here we study…
A measure of how sensitive the entanglement entropy is in a quantum system, has been proposed and its information geometric origin is discussed. It has been demonstrated for two exactly solvable spin systems, that thermodynamic criticality…
Relativistic continuous matrix product states (RCMPS) are a powerful variational ansatz for quantum field theories of a single field. However, they inherit a property of their non-relativistic counterpart that makes them divergent for…
Simulating models for quantum correlated matter unveils the inherent limitations of deterministic classical computations. In particular, in the case of quantum Monte Carlo methods, this is manifested by the emergence of negative weight…
Single parameter estimation is known to benefit from extreme sensitivity to parameter changes in quantum critical systems. However, the simultaneous estimation of multiple parameters is generally limited due to the incompatibility arising…
We study the behavior of the antiferromagnetic RP$^2$ model in $d=3$. The vacuum structure is analyzed in the critical and low temperature regions, paying special attention to the spontaneous symmetry breaking pattern. Near the critical…
The entanglement entropy of a pure quantum state of a bipartite system is defined as the von Neumann entropy of the reduced density matrix obtained by tracing over one of the two parts. Critical ground states of local Hamiltonians in one…
Deconfined criticality and gapless topological states have recently attracted growing attention, as both phenomena go beyond the traditional Landau paradigm. However, the deep connection between these two critical states, particularly in…
Studies of entanglement in many-particle systems suggest that most quantum critical ground states have infinitely more entanglement than non-critical states. Standard algorithms for one-dimensional many-particle systems construct model…
Using Quantum Monte Carlo simulations, we study the spin-1/2 Heisenberg model on a two-dimensional lattice formed by coupling diagonal ladders. The model hosts an antiferromagnetic N\'eel phase, a rung singlet product phase, and a…
The term Tensor Network States (TNS) refers to a number of families of states that represent different ans\"atze for the efficient description of the state of a quantum many-body system. Matrix Product States (MPS) are one particular case…