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arXiv:cond-mat/0401561

A close look at Jeckelmann's weak-coupling results: Reply to the Comment by Jeckelmann

G. P. Zhang

Published Jan 27, 2004• 0 citations
arXivHTMLPDF

Abstract

We are pleased to see that Jeckelmann has made many changes to the original version of his comment on our paper as a result of our response. Here is a copy of this powerful response that reveals problems in his previous results. However, since this response was written before his revised comment came out, new issues in his new comment, which will be commented if necessary, are not discussed at present. Although some changes are made in his new comment as we suggested in the response, we still see many other new and old misleading statements and results. We kindly suggest the author correct them since evidence is very compelling.

DOI
10.48550/arxiv.cond-mat/0401561

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Jeckelmann Replies:

Eric Jeckelmann

In their Comment (see cond-mat/0301237), Sandvik, Sengupta, and Campbell present some numerical evidences to support the existence of an extended bond-order-wave (BOW) phase at couplings (U,V) weaker than a tricritical point (U_t,V_t) in the ground state phase diagram of the one-dimensional half-filled U-V Hubbard model. They claim that their results do not agree with the phase diagram proposed in my Letter (cond-mat/0204244), which shows a BOW phase for couplings stronger than the critical point only. However, I argue here that their results are not conclusive and do not refute the phase diagram described in the Letter.

arXiv:cond-mat/0308446•Physical Review Letters•Aug 20, 2003•15 citations

On the weak coupling limit problem

Luigi Accardi, A. Frigerio, Yun Gang Lu

Lecture notes in mathematics•Jan 1, 1989•15 citations
We are pleased to see that Jeckelmann has made many changes to the original version of his comment on our paper as a result of our response. Here is a copy of this powerful response that reveals problems in his previous results. However, since this response was written before his revised comment came out, new issues in his new comment, which will be commented if necessary, are not discussed at present. Although some changes are made in his new comment as we suggested in the response, we still see many other new and old misleading statements and results. We kindly suggest the author correct them since evidence is very compelling.
This paper discusses perspectivism and relationalism in the two versions of Relational Quantum Mechanics (RQM): that initiated by Rovelli ( Int. J. Theor. Phys. , 35 (8), 1637–1678 1996) and the other, by Adlam and Rovelli ( Philos. Phys. , 1 (1) 2023). To this end, we offer a substantial discussion of this interpretation. We investigate the issue of the disagreement of results between different observers; distinguish four senses of agreement: strong, weak, very weak, and perspectival; and argue that the old version guarantees only the very weak and perspectival agreement, whereas the new version guarantees the weak agreement as well. The problem that individuals in RQM need to be propertyless when they do not interact is also investigated. Concerning the issue of probabilities in RQM, we argue that to express probabilities involving events relative to different systems, a new kind of probability spaces needs to be devised. The final problem that we identify concerns underspecified dynamics; we argue that some additional postulates are indispensable to make RQM’s dynamics fully specified. The last two points lead to the conclusion that, contrary to declarations of RQM proponents, this interpretation requires some modifications of quantum formalism and not merely conceptual changes. Finally, concerning the problem of testimony, while the new version of RQM was devised to solve it, we argue that in the old version, this problem can be alleviated to the extent that perspectivism permits.
In their Comment (see cond-mat/0301237), Sandvik, Sengupta, and Campbell present some numerical evidences to support the existence of an extended bond-order-wave (BOW) phase at couplings (U,V) weaker than a tricritical point (U_t,V_t) in the ground state phase diagram of the one-dimensional half-filled U-V Hubbard model. They claim that their results do not agree with the phase diagram proposed in my Letter (cond-mat/0204244), which shows a BOW phase for couplings stronger than the critical point only. However, I argue here that their results are not conclusive and do not refute the phase diagram described in the Letter.