We introduce a class of states, called minimally entangled typical thermal states, designed to resemble a typical state of a quantum system at finite temperature with a bias towards classical ...(minimally entangled) properties. These states reveal in an intuitive way properties such as short-range order which may often be hidden. A finite-T density matrix renormalization group algorithm is presented which is only modestly slower than the T=0 density matrix renormalization group.
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Ground-state phase diagram of the t-t ' -J model Jiang, Shengtao; Scalapino, Douglas J; White, Steven R
Proceedings of the National Academy of Sciences - PNAS,
11/2021, Volume:
118, Issue:
44
Journal Article
Peer reviewed
Open access
We report results of large-scale ground-state density matrix renormalization group (DMRG) calculations on t-Formula: see text-J cylinders with circumferences 6 and 8. We determine a rough phase ...diagram that appears to approximate the two-dimensional (2D) system. While for many properties, positive and negative Formula: see text values (Formula: see text) appear to correspond to electron- and hole-doped cuprate systems, respectively, the behavior of superconductivity itself shows an inconsistency between the model and the materials. The Formula: see text (hole-doped) region shows antiferromagnetism limited to very low doping, stripes more generally, and the familiar Fermi surface of the hole-doped cuprates. However, we find Formula: see text strongly suppresses superconductivity. The Formula: see text (electron-doped) region shows the expected circular Fermi pocket of holes around the Formula: see text point and a broad low-doped region of coexisting antiferromagnetism and d-wave pairing with a triplet p component at wavevector Formula: see text induced by the antiferromagnetism and d-wave pairing. The pairing for the electron low-doped system with Formula: see text is strong and unambiguous in the DMRG simulations. At larger doping another broad region with stripes in addition to weaker d-wave pairing and striped p-wave pairing appears. In a small doping region near Formula: see text for Formula: see text, we find an unconventional type of stripe involving unpaired holes located predominantly on chains spaced three lattice spacings apart. The undoped two-leg ladder regions in between mimic the short-ranged spin correlations seen in two-leg Heisenberg ladders.
We use the density matrix renormalization group to perform accurate calculations of the ground state of the nearest-neighbor quantum spin S = 1/2 Heisenberg antiferromagnet on the kagome lattice. We ...study this model on numerous long cylinders with circumferences up to 12 lattice spacings. Through a combination of very-low-energy and small finite-size effects, our results provide strong evidence that, for the infinite two-dimensional system, the ground state of this model is a fully gapped spin liquid.
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We establish a precise connection between discrete wavelet transforms and entanglement renormalization, a real-space renormalization group transformation for quantum systems on the lattice, in the ...context of free particle systems. Specifically, we employ Daubechies wavelets to build approximations to the ground state of the critical Ising model, then demonstrate that these states correspond to instances of the multiscale entanglement renormalization ansatz (MERA), producing the first known analytic MERA for critical systems.
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A recent blog post on the SEDA educational development forum led to a stimulating discussion about whether learning should be fun (Saunders, 2022). As learning developers, it makes sense to make ...learning activities enjoyable for students where we can. However, this lightning talk contended that some aspects of learning are unlikely to - and perhaps even cannot - be fun. Indeed, we may limit the inclusiveness of our approach if we fail to address this idea in our work. As such, it is important for learning developers to be clear with students that some aspects of their learning experience may involve struggle and discomfort.
Whilst it is pleasant for us when students end interactions with learning developers feeling reassured and with a smile on their face, it may at times be more helpful to see them leave with a look of grim determination. For example, threshold concepts scholarship identifies dimensions of learning that may require transformation not only of one’s understanding but also elements of one’s identity. Wrangling with troublesome knowledge within often uncomfortable liminal states of ‘in-betweenness’ is therefore necessary for students to progress in their understanding or ability (Land et al., 2008).
Drawing on recent educational and learning development discourse, in this talk White argued that recognising that learning cannot always be fun is important in creating an inclusive learning experience for students. Indeed, students can take comfort, confidence, and even a sense of belonging from understanding that their peers and lecturers struggle with some aspects of learning. At times, we may need to ‘suffer now’ to gain satisfaction and achievement in the longer term. We need to be up front about this in our interactions with students.
Threshold concepts (TCs) represent pivotal ‘eureka’ moments in learning, where a person makes a leap in understanding or ability ‘akin to a portal, opening up a new and previously inaccessible way of ...thinking about something’ (Meyer and Land, 2003, p. 1). Crossing these thresholds can be transformative, integrative, and irreversible, but also troublesome. Discussion of threshold concepts may provide a novel way of surfacing the core challenges of learning development work—whether in terms of helping students to progress or informing how we operate within the university context.
Research in learning development has identified ‘generic’ threshold concepts that students might need to support their studies. However, it is also worth considering whether we as learning developers can collectively identify threshold concepts that increase our impact when working with students, academics, and other stakeholders. This session contextualised the idea by first looking at threshold concepts for student development. This activity aimed to enhance participants’ understanding of threshold concepts.
We propose an improved scheme to do the time-dependent variational principle (TDVP) in finite matrix product states (MPSs) for two-dimensional systems or one-dimensional systems with long-range ...interactions. We present a method to represent the time-evolving state in a MPS with its basis enriched by state averaging with global Krylov vectors. We show that the projection error is significantly reduced so precise time evolution can still be obtained even if a larger time step is used. Combined with the one-site TDVP, our approach provides a way to dynamically increase the bond dimension while still preserving unitarity for real-time evolution. Our method can be more accurate and exhibit slower bond dimension growth than the conventional two-site TDVP.
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•This study explores how entrepreneurs introducing a new organizational form can build legitimacy and capabilities to overcome significant liabilities of newness, and how their actions and the ...institutional structure co-evolve.•Our multiple case study design enabled us to explicate specific actions that entrepreneurs founding China's private solar photovoltaic (PV) firms took as they built organizational capabilities and established their legitimacy vis-à-vis resource holders and global markets.•We identified three legitimacy-based strategies they used: leveraging their existing sources of legitimacy, aligning their actions with established institutional rules, norms and beliefs, and enacting the institutional environment to change perceptions of what is legitimate.•The nature of entrepreneurial action differs significantly among the firms, with the early entrants (the “explorers”) needing to overcome far greater challenges in gathering critical resources and capabilities and establishing their legitimacy, both domestically and internationally, than the later entrants (the “exploiters”).•Our findings also suggest that the government, through its policies and actions, can create an environment in which experimentation and exploration is legitimate, thereby making it easier for entrepreneurs, new ventures and new organizational forms to access critical resources and realize their potential.
This study explores how entrepreneurs introducing a new organizational form can build legitimacy and capabilities to overcome significant liabilities of newness, and how their actions and the institutional structure co-evolve. Our multiple case study design enabled us to explicate specific actions that entrepreneurs founding China's private solar photovoltaic (PV) firms took as they built organizational capabilities and established their legitimacy vis-à-vis resource holders and global markets. We identified three legitimacy-based strategies they used: leveraging their existing sources of legitimacy, aligning their actions with established institutional rules and norms, and enacting the institutional environment to change perceptions of what is legitimate. We also found a stark contrast between the early and late entrants. The early entrants had to build an effective organizational capability and establish their own firm's legitimacy, as well as establish the legitimacy of the private Chinese solar PV firm as a viable organizational form, both domestically and abroad. Later entrants could leverage the legitimacy established by the early entrants, enabling them to more easily and quickly access external resources and become competitive. Our findings also suggest an important role for government in promoting and supporting entrepreneurship that complements well-established approaches. Namely, through its policies and actions, the government can create an environment in which experimentation and exploration is legitimate, thereby making it easier for entrepreneurs, new ventures and new organizational forms to access critical resources and realize their potential.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
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