Michigan State University and University of California, Davis researchers have mapped the parent Hamiltonians of a novel class of quantum states, revealing a departure from established principles in condensed matter physics. Unlike traditional models built on uniform states, the team investigated ergodic Matrix Product States (EMPS) defined by site-dependent random tensors, introducing variability at every point along a quantum spin chain. Their work demonstrates that, unlike translation-invariant systems, the parent Hamiltonians for these EMPS challenge the typical expectation that frustration-free ground states exhibit an energy gap. Owen Ekblad and colleagues show that the thermodynamic limit of an EMPS is the unique frustration-free ground state of a parent Hamiltonian, opening new avenues for exploring complex quantum systems without relying on a gap in energy levels.
A new understanding of quantum entanglement reveals that frustration-free ground states don’t always require an energy gap, challenging a long-held assumption within condensed matter physics. Unlike traditional, translation-invariant models, these EMPS utilize statistical variation at each location. This isn’t simply a ground state, but the unique frustration-free ground state of a parent Hamiltonian on the whole spin chain, provided this condition is met. The team’s approach builds on the established framework of Matrix Product States, originally formulated to investigate the AKLT antiferromagnet, but extends it to encompass systems with MPS used as a reverse-engineered approach to studying arbitrary local Hamiltonians by first approximating ground states of these interactions with MPS and then studying directly their parent Hamiltonians. The resulting parent Hamiltonians may not be finite-range, meaning their influence doesn’t diminish predictably with distance, a key distinction from translation-invariant systems.
These states efficiently approximate the lowest energy levels of quantum spin chains, but recent research at Michigan State University and University of California, Davis expands beyond traditional, translation-invariant models to explore ergodic MPS (EMPS). Crucially, the validity of this finding rests on ensuring the local MPS is injective. This condition, if met, guarantees the existence of a unique ground state. The team’s work suggests that the resulting Hamiltonian may not always be finite-range, challenging established assumptions about the relationship between MPS and their parent Hamiltonians.
Researchers from Michigan State University and University of California, Davis are pushing the boundaries of matrix product state (MPS) modeling with a new approach to simulating quantum systems. Their work centers on ergodic matrix product states (EMPS), a departure from traditional, translation-invariant models. Unlike conventional MPS which utilize uniform states, these EMPS are defined by introducing variability at every point along the spin chain. This statistical variation allows for exploration of systems previously inaccessible to standard techniques. A key finding challenges a long-held assumption in the field: parent Hamiltonians for these EMPS may not be gapped, which is surprising because frustration-free ground states typically exhibit a gap in their energy spectra. The team’s analysis reveals that the absence of a gap isn’t a flaw, but a natural consequence of the EMPS’s inherent randomness. They show the thermodynamic limit of an EMPS is the unique frustration-free ground state of a parent Hamiltonian on the whole spin chain, which, depending on the statistical properties of the EMPS, may or may not be finite-range.
The pursuit of accurately modeling complex quantum systems has led researchers from Michigan State University and University of California, Davis to explore matrix product states (MPS) beyond traditional, translation-invariant frameworks. This departure from uniformity allows for the investigation of systems previously inaccessible to standard MPS methods. This isn’t merely establishing a ground state, but proving it’s the only one, given the specified condition. Owen Ekblad at Michigan State University, and colleagues show that the thermodynamic limit of an EMPS is the unique frustration-free ground state of a parent Hamiltonian on the whole spin chain.
The conventional understanding of quantum ground states assumes a degree of uniformity; however, recent work challenges this, revealing a surprising level of variability even in seemingly ordered systems. Researchers at Michigan State University and the University of California, Davis, have been mapping the parent Hamiltonians of ergodic Matrix Product States (EMPS), uncovering properties that diverge from traditional models. This departure from translation-invariant systems has significant implications. The team shows the thermodynamic limit of an EMPS is the unique frustration-free ground state of a parent Hamiltonian on the whole spin chain, which, depending on the statistical properties of the EMPS, may or may not be finite-range. The conventional picture of matrix product states (MPS) as ground states of local, gapped Hamiltonians is challenged by recent work revealing a surprising flexibility in their parent Hamiltonians.
The pursuit of understanding quantum materials has increasingly focused on matrix product states (MPS) as representations of their ground states, yet most investigations remain within translationally-invariant systems. Recent work, however, explores a more complex scenario: ergodic MPS (EMPS), defined by site-dependent random tensors {Xj[k]}j=1D, introducing variability along the spin chain not seen in traditional models. This shift in perspective challenges long-held assumptions about the nature of parent Hamiltonians, the local interactions that give rise to these states. Researchers from Michigan State University and University of California, Davis demonstrated this by constructing an EMPS that isn’t the ground state of any gapped finite-range interaction, a stark contrast to the behavior of translationally-invariant MPS.
This departure from translation-invariant systems allows for the exploration of more complex quantum phenomena, particularly those found in disordered materials. This means the energy levels of these systems don’t necessarily exhibit a gap, opening possibilities for studying gapless systems previously inaccessible through conventional MPS techniques. This uniqueness is significant, as it establishes a direct link between the statistical properties of the EMPS and the Hamiltonian governing its behavior. MPS are used as a reverse-engineered approach to studying arbitrary local Hamiltonians by first approximating ground states of these interactions with MPS and then studying directly their parent Hamiltonians.
The exploration of ergodic Matrix Product States (EMPS) is yielding surprising insights into the nature of quantum systems, moving beyond the limitations of traditional, translation-invariant models. Researchers at Michigan State University and University of California, Davis demonstrate that EMPS parent Hamiltonians can exist without this gap, opening up possibilities for studying previously inaccessible gapless systems. This contrasts with many physical systems where interactions are short-ranged. These findings suggest a new framework for modeling complex quantum phenomena, where statistical properties play a crucial role in determining system behavior.
Source: https://arxiv.org/abs/2607.01446
